on the accuracy and resolvability of vector parameter estimates in this paper we address the problem of fundamental limitations on resolution in deterministic parameters estimation we introduce a definition of resolvability based on probability and incorporating a requirement for accuracy unlike most existing definitions indeed in many application the key problem is to obtain distributions of estimates that are not only distinguishable but also accurate and compliant with a required precision we exemplify the proposed definition with estimators that produce normal estimates as in the conditional model for which the gaussianity and efficiency of maximum likelihood estimators mles in the asymptotic region of operation in terms of signal to noise ratio and or in large number of snapshots is well established even for a single snapshot in order to measure the convergence in distribution we derive a simple test allowing to check whether the conditional mles operate in the asymptotic region of operation last we discuss the resolution of two complex exponentials with closely spaced frequencies and compare the results obtained with the ones provided by the various statistical resolution limit released in the open literature

on the cr structure of compact group orbits associated with bounded symmetric domains let e be a complex vector space of finite dimension and let k gl e be a compact connected subgroup then for fixed a e the orbit k k a is a real analytic submanifold of e that inherits various structures from e for instance choosing a k invariant positive definite inner product x y on e makes k a riemannian manifold on which k acts transitively by isometries on the other hand k inherits from e a cauchy riemann structure cr structure that is given by the distribution of the maximal complex subspaces hx k tx k itx k of the real tangent spaces tx k e x k together with the complex structure on every hx k multiplication by i the subspace hx k is called the holomorphic tangent space to k at x see 9 and 4 as general references for cr manifolds of interest for the geometry of the orbit k k a with respect to its cr structure is the study of the cr functions or more generally cr mappings on k i e of smooth functions f k c that satisfy the tangential cauchy riemann differential equations in the sense that the restriction of the differential df to every holomorphic tangent space is complex linear for instance all holomorphic functions defined in an open neighbourhood of k e give by restriction real analytic cr functions on k actually we deal with the more general continuous cr functions on k which satisfy by definition the tangential cr equations in the distribution sense or equivalently which are locally uniform limits of sequences of smooth cr functions due to the approximation theorem of baouenditreves 6 in this context it is of interest to determine the space of all

on the resolvability of normally distributed vector parameter estimates this paper presents a metric useful in analyzing the resolution of multidimensional vector parameter estimators that produce normal estimates this metric is based on the distance between ellipsoidal confidence regions about each of the parameters when the ellipsoids are disjoint the parameters are deemed resolvable this paper presents a method for finding the noise level at which all of the ellipsoids are disjoint but at least two are tangent this is deemed the resolution threshold noise level the underlying mathematical result treats the problem of finding a dilation noise level at which two coupled quadratic equations have a unique solution

convergence of formal cr mappings into strongly pseudoconvex cauchy riemann manifolds it is shown that any formal holomorphic mapping sending a real analytic generic submanifold m subset mathbb c n of finite type into a real analytic strongly pseudoconvex cr submanifold m subset mathbb c n is necessarily convergent as a consequence we obtain a positive answer to the long standing open question of whether formal holomorphic maps sending real analytic strongly pseudoconvex hypersurfaces into each other are convergent

rigidity of proper holomorphic maps between bounded symmetric domains our first main result gives assumptions guaranteeing that proper holomorphic maps between cartan type i bounded symmetric domains have simple block matrix shape answering positively a question of mok the proof is based on the second main result establishing similar phenomenon for local cr maps between arbitrary boundary components of two bounded symmetric domains of the above type since boundary components other than shilov boundaries are levi degenerate our analysis is based on their 2 nondegeneracy combining levi forms with higher order tensors

partial rigidity of degenerate cr embeddings into spheres abstract in this paper we study degenerate cr embeddings f of a strictly pseudoconvex hypersurface m c n 1 into a sphere s in a higher dimensional complex space c n 1 the degeneracy of the mapping f will be characterized in terms of the ranks of the cr second fundamental form and its covariant derivatives in 2004 the author together with x huang and d zaitsev established a rigidity result for cr embeddings f into spheres in low codimensions a key step in the proof of this result was to show that degenerate mappings are necessarily contained in a complex plane section of the target sphere partial rigidity in the 2004 paper it was shown that if the total rank d of the second fundamental form and all of its covariant derivatives is n here n is the cr dimension of m then f m is contained in a complex plane of dimension n d 1 the converse of this statement is also true as is easy to see when the total rank d exceeds n it is no longer true in general that f m is contained in a complex plane of dimension n d 1 as can be seen by examples in this paper we carry out a systematic study of degenerate cr mappings into spheres we show that when the ranks of the second fundamental form and its covariant derivatives exceed the cr dimension n then partial rigidity may still persist but there is a defect k that arises from the ranks exceeding n such that f m is only contained in a complex plane of dimension n d k 1 moreover this defect occurs in general as is illustrated by examples

a reflection principle with applications to proper holomorphic mappings j l holomorphic mappings from b into b k we then apply this principle to the problem of characterizing the proper holomorphic mappings from b into b k two such mappings f and g are said to be equivalent if there exist holomorphic automorphisms b and p of b and bk respectively such that f pogo49 there are at present three significant papers on the subject the first by alexander 1 proves that i f f is a proper holomorphic mapping of b into b then f is a holomorphic automorphism of b webster i 5 proved that for n 3 i f f is a proper holomorphic mapping of b into b 1 which is c3 then f maps b into a hyperplane in r hence using alexander s result and properties of the holomorphic automorphisms f is equivalent to the mapping zl z2 z zi z2 zn o alexander s example zl z2 z2 zlz2 z 2 shows that webster s result does not hold for n 2 in a recent paper faran 2 has characterized all proper holomorphic mappings f from b 2 to b 3 that satisfy the additional smoothness condition fec3 2 he proves that such mappings are equivalent to one of the four mappings z w z w 0 z w z zw w2 z w r z 2 l zw w2

proper holomorphic mappings from the two ball to the three ball we prove that a proper mapping of the two ball in cn into the three ball which is c2 on the closed two ball is equivalent to one of four normalized polynomial mappings this improves the known result of faran the proof is basic using taylor expansions

strongly pseudoconvex domains as subvarieties of complex manifolds in this paper we obtain existence and approximation results for closed complex subvarieties that are normalized by strongly pseudoconvex stein domains our sufficient condition for the existence of such subvarieties in a complex manifold x is expressed in terms of the morse indices and the number of positive levi eigenvalues of an exhaustion function on x examples show that our conditions cannot be weakened in general we obtain optimal results for subvarieties of this type in complements of compact complex submanifolds with griffiths positive normal bundle in the projective case these generalize classical theorems of remmert bishop and narasimhan concerning proper holomorphic maps and embeddings to bbb c n bbb p n backslash bbb p n 1

on the convegence of a sequential penalty function method for constrained minimization the convergence behaviour of a class of iterative methods for solving the constrained minimization problem is analysed the methods are based on the sequential minimization of a simple differentiable penalty function they are sufficiently general to ensure global convergence of the iterates to the solution of the problem at an asymptotic two step q superlinear rate

convergence and divergence of formal cr mappings let m subset mathbb c n be a generic real analytic submanifold of finite type m subset mathbb c n be a real analytic set and p in m where we assume that n n geqslant 2 let h mathbb c n p to mathbb c n be a formal holomorphic mapping sending m into m and let mathcal e m denote the set of points in m through which there passes a complex analytic subvariety of positive dimension contained in m we show that if h does not send m into mathcal e m then h must be convergent as a consequence we derive the convergence of all formal holomorphic mappings when m does not contain any complex analytic subvariety of positive dimension answering by this a long standing open question in the field more generally we establish necessary conditions for the existence of divergent formal maps even when the target real analytic set is foliated by complex analytic subvarieties allowing us to settle additional convergence problems such as e g for transversal formal maps between levi non degenerate hypersurfaces and for formal maps with range in the tube over the light cone

local holomorphic mappings respecting homogeneous subspaces on rational homogeneous spaces let g p be a rational homogeneous space not necessarily irreducible and x 0 in g p be the point at which the isotropy group is p the g translates of the orbit qx 0 of a parabolic subgroup q subsetneq g such that p cap q is parabolic are called q cycles we established an extension theorem for local biholomorphisms on g p that map local pieces of q cycles into q cycles we showed that such maps extend to global biholomorphisms of g p if g p is q cycle connected or equivalently if there does not exist a non trivial parabolic subgroup containing p and q then we applied this to the study of local biholomorphisms preserving the real group orbits on g p and showed that such a map extend to a global biholomorphism if the real group orbit admits a non trivial holomorphic cover by the q cycles the non closed boundary orbits of a bounded symmetric domain embedded in its compact dual are examples of such real group orbits finally using the results of mok zhang on schubert rigidity we also established a cartan fubini type extension theorem pertaining to q cycles saying that if a local biholomorphism preserves the variety of tangent spaces of q cycles then it extends to a global biholomorphism when the q cycles are positive dimensional and g p is of picard number 1 this generalizes a well known theorem of hwang mok on minimal rational curves

initial monomial invariants of holomorphic maps we study a new biholomorphic invariant of holomorphic maps between domains in different dimensions based on generic initial ideals we start with the standard generic monomial ideals to find invariants for rational maps of spheres and hyperquadrics giving a readily computable invariant in this important case for example the generic initial monomials distinguish all four inequivalent rational proper maps from the two to the three dimensional ball next we associate to each subspace x subset mathcal o u a generic initial monomial subspace which is invariant under biholomorphic transformations and multiplication by nonzero functions the generic initial monomial subspace is a biholomorphic invariant for holomorphic maps if the target automorphism is linear fractional as in the case of automorphisms of spheres or hyperquadrics

rigidity of cr maps between shilov boundaries of bounded symmetric domains our goal is to establish what seems to be the first rigidity result for cr embeddings between shilov boundaries of bounded symmetric domains of higher rank the result states that any such cr embedding is the standard linear embedding up to cr automorphisms our basic assumption extends precisely the well known optimal bound for the rank one case there are no other restrictions on the ranks in particular the difficult case when the target rank is larger than the source rank is also allowed

volume preserving mappings between hermitian symmetric spaces of compact type abstract in this paper we establish the rigidity result for local holomorphic volume preserving maps from an irreducible hermitian symmetric space of compact type into its cartesian products

statistical resolution limits and the complexified crame spl acute r rao bound array resolution limits and accuracy bounds on the multitude of signal parameters e g azimuth elevation doppler range cross range depth frequency chirp polarization amplitude phase etc estimated by array processing algorithms are essential tools in the evaluation of system performance the case in which the complex amplitudes of the signals are unknown is of particular practical interest a computationally efficient formulation of these bounds from the perspective of derivations and analysis is presented for the case of deterministic and unknown signal amplitudes a new derivation is given using the unknown complex signal parameters and their complex conjugates the new formula is readily applicable to obtaining either symbolic or numerical solutions to estimation bounds for a very wide class of problems encountered in adaptive sensor array processing this formula is shown to yield several of the standard crame spl acute r rao results for array processing along with new results of fundamental interest specifically a new closed form expression for the statistical resolution limit of an aperture for any asymptotically unbiased superresolution algorithm e g music esprit is provided the statistical resolution limit is defined as the source separation that equals its own crame spl acute r rao bound providing an algorithm independent bound on the resolution of any high resolution method it is shown that the statistical resolution limit of an array or coherent integration window is about 1 2 spl middot snr sup 1 4 relative to the fourier resolution limit of 2 spl pi n radians large number n of array elements that is the highest achievable resolution is proportional to the reciprocal of the fourth root of the signal to noise ratio snr in contrast to the square root snr sup 1 2 dependence of standard accuracy bounds these theoretical results are consistent with previously published bounds for specific superresolution algorithms derived by other methods it is also shown that the potential resolution improvement obtained by separating two collinear arrays synthetic ultra wideband each with a fixed aperture b wavelengths by m wavelengths assumed large is approximately m b sup 1 2 in contrast to the resolution improvement of m b for a full aperture exact closed form results for these problems with their asymptotic approximations are presented

the hartogs type extension theorem for meromorphic maps into compact kahler manifolds extension theorems of this type are often called hartogs type extension theorems the above result was conjectured by griffiths see problem 1 in gr who proved it in the special case when d p o i n t and f d x is holomorphic important contributions towards the proof of this conjecture were made by b shiffman y t siu n sibony see sh sil sb3 in particular y t siu proved a thullen type extension theorem for meromorphic maps into compact kfihler manifolds see w 1 the above theorem can be applied to the study of covering maps of zariski open subsets in compact kfihler manifolds recall that a subdomain d of a complex manifold m is called levi pseudoconvex if for any peod there exists a neighbourhood u of p in m such that u c d is stein we say that d covers a complex manifold x if there is a subgroup g c aut d acting properly discontinuously and freely on d with d g x

the equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics we consider the class of levi nondegenerate hypersurfaces m in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i that admit a local cr transversal embedding near a point p e m into a standard nondegenerate hyperquadric in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i with codimension k n n small compared to the cr dimension n of m we show that for hypersurfaces in this class there is a normal form which is closely related to the embedding such that any local equivalence between two hypersurfaces in normal form must be an automorphism of the associated tangent hyperquadric we also show that if the signature of m and that of the standard hyperquadric in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i are the same then the embedding is rigid in the sense that any other embedding must be the original embedding composed with an automorphism of the quadric

rigidity of proper holomorphic mappings between certain unbounded non hyperbolic domains abstract the fock bargmann hartogs domain d n m 0 in c n m is defined by the inequality w 2 e z 2 where z w c n c m which is an unbounded non hyperbolic domain in c n m recently yamamori gave an explicit formula for the bergman kernel of the fock bargmann hartogs domains in terms of the polylogarithm functions and kim ninh yamamori determined the automorphism group of the domain d n m in this article we obtain rigidity results on proper holomorphic mappings between two equidimensional fock bargmann hartogs domains our rigidity result implies that any proper holomorphic self mapping on the fock bargmann hartogs domain d n m with m 2 must be an automorphism

holomorphic mappings between hyperquadrics with small signature difference in this paper we study holomorphic mappings sending a hyperquadric of signature ell in bbb c n into a hyperquadric of signature ell in bbb c n we show theorem 1 1 that if the signature difference ell ell is not too large then the mapping can be normalized by automorphisms of the target hyperquadric to a particularly simple form and in particular the image of the mapping is contained in a complex plane of a dimension that depends only on ell and ell and not on the target dimension n we also prove a hopf lemma type result theorem 1 3 for such mappings

bounding the rank of hermitian forms and rigidity for cr mappings of hyperquadrics using green s hyperplane restriction theorem we prove that the rank of a hermitian form on the space of holomorphic polynomials is bounded by a constant depending only on the maximum rank of the form restricted to affine manifolds as an application we prove a rigidity theorem for cr mappings between hyperquadrics in the spirit of the results of baouendi huang and baouendi ebenfelt huang given a real analytic cr mapping of a hyperquadric not equivalent to a sphere to another hyperquadric q a b either the image of the mapping is contained in a complex affine subspace or a is bounded by a constant depending only on b finally we prove a stability result about existence of nontrivial cr mappings of hyperquadrics that is as long as both a and b are sufficiently large and comparable then there exist cr mappings whose image is not contained in a hyperplane the rigidity result also extends when mapping to hyperquadrics in infinite dimensional hilbert space

rigidity of proper holomorphic self mappings of the pentablock abstract the pentablock is a hartogs domain in c 3 over the symmetrized bidisc in c 2 the domain is a bounded inhomogeneous pseudoconvex domain which does not have a c 1 boundary recently agler lykova young constructed a special subgroup of the group of holomorphic automorphisms of the pentablock and kosinski fully described the group of holomorphic automorphisms of the pentablock the aim of the present study is to prove that any proper holomorphic self mapping of the pentablock must be an automorphism

regularity of mappings into classical domains we study the regularity and algebraicity for mappings into classical domains among other things we establish everywhere regularity and algebraicity results for c 2 cr maps into the set of smooth boundary points of a classical domain where the codimension can be arbitrarily large

an iterative l_ 1 based image restoration algorithm with an adaptive parameter estimation regularization methods for the solution of ill posed inverse problems can be successfully applied if a right estimation of the regularization parameter is known in this paper we consider the l1 regularized image deblurring problem and evaluate its solution using the iterative forward backward splitting method based on this approach we propose a new adaptive rule for the estimation of the regularization parameter that at each iteration dynamically updates the parameter value following the evolution of the objective functional the iterative algorithm automatically stops without requiring any assumption about the perturbation process when the parameter has reached a seemingly near optimal value in spite of the fact that the optimality of this value has not yet been theoretically proved a large number of numerical experiments confirm that the proposed rule yields restoration results competitive with those of the best state of the art algorithms

on the embeddability of real hypersurfaces into hyperquadrics abstract a well known result of forstneric 15 states that most real analytic strictly pseudoconvex hypersurfaces in complex space are not holomorphically embeddable into spheres of higher dimension a more recent result by forstneric 16 states even more most real analytic hypersurfaces do not admit a holomorphic embedding even into a merely algebraic hypersurface of higher dimension in particular a hyperquadric we emphasize that both cited theorems are proved by showing that the set of embeddable hypersurfaces is a set of first baire category at the same time the classical theorem of webster 30 asserts that every real algebraic levi nondegenerate hypersurface admits a transverse holomorphic embedding into a nondegenerate real hyperquadric in complex space in this paper we provide effective results on the non embeddability of real analytic hypersurfaces into a hyperquadric we show that under the codimension restriction n 2 n the defining functions z z u of all real analytic hypersurfaces m v z z u c n 1 containing levi nondegenerate points and locally transversally holomorphically embeddable into some hyperquadric q c n 1 satisfy an universal algebraic partial differential equation d 0 where the algebraic differential operator d d n n depends on n 1 n n 2 n only to the best of our knowledge this is the first effective result characterizing real analytic hypersurfaces embeddable into a hyperquadric of higher dimension as an application we show that for every n n as above there exists n n such that a zariski generic real analytic hypersurface m c n 1 of degree is not transversally holomorphically embeddable into any hyperquadric q c n 1 we also provide an explicit upper bound for in terms of n n to the best of our knowledge this gives the first effective lower bound for the cr complexity of a zariski generic real algebraic hypersurface in complex space of a fixed degree

a robust approach for high resolution frequency estimation a robust estimation method for frequencies of received signals is considered the influence function of a robust estimate is derived for the sinusoidal signals the variance of the robust estimate is also derived using the influence function it is found that the robust estimate attains the cramer rao lower bound crlb for the contaminated gaussian distribution it is of order o n sup 3 and is close to the crlb for the perfect gaussian distribution the authors introduce some basic definitions for the high resolution frequency estimation method and prove that the robust estimate has the high resolution property this property is also confirmed by numerical simulations

a construction of inner functions on the unit ball in c p in their recent paper 1 hakim and sibony came very close to constructing inner functions on the unit ball in c e in fact only some minor modifications of their arguments are necessary to produce bona fide inner functions the present paper carries out these modifications since we need to point out some information not explicitly stated but clear from the context in their paper and to make the exposition self contained we repeat most of the material in their paper our lemma 1 for instance is identical to their lemma 3 and our application of lemma 1 in the proof of lemma 2 is the same as theirs in the proof of theorem 1 the following notations are used b is the unit ball in c p br z cp izl r we use the distance

d angelo conjecture in the third gap interval we show that the d angelo conjecture holds in the third gap interval more precisely we prove that the degree of any rational proper holomorphic map from mathbb b n to mathbb b 4n 6 with n ge 7 is not more than 3

on the regularity of cr mappings between cr manifolds of hypersurface type we prove smooth and analytic versions of the classical schwarz reflection principle for transversal cr mappings between two levi nondegenerate cr manifolds of hypersurface type

fixed point continuation for ell_1 minimization methodology and convergence we present a framework for solving the large scale ell 1 regularized convex minimization problem min x 1 mu f x our approach is based on two powerful algorithmic ideas operator splitting and continuation operator splitting results in a fixed point algorithm for any given scalar mu continuation refers to approximately following the path traced by the optimal value of x as mu increases in this paper we study the structure of optimal solution sets prove finite convergence for important quantities and establish q linear convergence rates for the fixed point algorithm applied to problems with f x convex but not necessarily strictly convex the continuation framework motivated by our convergence results is demonstrated to facilitate the construction of practical algorithms

dimension and rigidity of quasi fuchsian representations let fo c so n 1 n 2 be a cocompact lattice and p fo f be an injective representation into a convex cocompact discrete isometric subgroup of a noncompact rank 1 symmetric space the hausdorff dimension 6 f of the limit set of f p fo satisfies 6 f 6 fo n 1 we prove that equality holds if and only if p is a fuchsian representation i e f preserves a totally geodesic copy of hri in hr this generalizes the result of 2 and settles a question raised by tukia 43 p 428 actually we prove a more general result in the context of variable negative curvature strikingly there are no quasi fuchsian representations at least for the lower codimensional case in complex hyperbolic geometry that is for a cocompact lattice fo c su n 1 n 2 and an injective representation p fo su m 1 n m 2n 1 with f p fo convex cocompact we prove that one always has 6 f 6 fo and moreover f must stabilize a totally geodesic copy of h in h this can be viewed as a global generalization of goldman and millson s local rigidity theorem see 20 another global generalization was obtained by k corlette 5 various other related rigidity results are also obtained

local embeddability of cr manifolds into spheres in this paper we solve local cr embeddability problem of smooth cr manifolds into spheres under a certain nondegeneracy condition on the chern moser s curvature tensor we state necessary and sufficient conditions for the existence of cr embeddings as finite number of equations and rank conditions on the chern moser s curvature tensors and their derivatives we also discuss the rigidity of those embeddings

two dimensional prony modeling and parameter estimation a new method for estimating the two dimensional 2d exponential modes and amplitude coefficients in a prony model is presented this method involves two parts each utilizing a 1d singular value decomposition based technique and is capable of locating frequencies anywhere in the 2d frequency plane simulations are shown which demonstrate the performance of the algorithm

a fast multilevel algorithm for wavelet regularized image restoration we present a multilevel extension of the popular ldquothresholded landweberrdquo algorithm for wavelet regularized image restoration that yields an order of magnitude speed improvement over the standard fixed scale implementation the method is generic and targeted towards large scale linear inverse problems such as 3 d deconvolution microscopy the algorithm is derived within the framework of bound optimization the key idea is to successively update the coefficients in the various wavelet channels using fixed subband adapted iteration parameters step sizes and threshold levels the optimization problem is solved efficiently via a proper chaining of basic iteration modules the higher level description of the algorithm is similar to that of a multigrid solver for pdes but there is one fundamental difference the latter iterates though a sequence of multiresolution versions of the original problem while in our case we cycle through the wavelet subspaces corresponding to the difference between successive approximations this strategy is motivated by the special structure of the problem and the preconditioning properties of the wavelet representation we establish that the solution of the restoration problem corresponds to a fixed point of our multilevel optimizer we also provide experimental evidence that the improvement in convergence rate is essentially determined by the unconstrained linear part of the algorithm irrespective of the type of wavelet finally we illustrate the technique with some image deconvolution examples including some real 3 d fluorescence microscopy data

rigidity of proper holomorphic mappings between nonequidimensional bounded symmetric domains we prove that any proper holomorphic mapping from d p p 1 i to d p p i p geq 3 is necessarily a totally geodesic isometric embedding with respect to their bergman metrics and therefore is the standard linear embedding up to their automorphisms the proof of the main result in this paper will be achieved by a differential geometric study of a special class of complex geodesic curves on the bounded symmetric domains with respect to their bergman metrics

rigidity and holomorphic segre transversality for holomorphic segre maps let mathcal h n and mathcal h mathcal n denote the complexifications of heisenberg hypersurfaces in mathbf c n and mathbf c n respectively we show that non degenerate holomorphic segre mappings from mathcal h n into mathcal h n with n leq2n 2 possess a partial rigidity property as an application we prove that the holomorphic segre non transversality for a holomorphic segre map from mathcal h n into mathcal h n with n leq2n 2 propagates along segre varieties we also give an example showing that this propagation property of holomorphic segre transversality fails when n 2n 2

on the performance of signal subspace processing part i narrow band systems this paper presents an analytical evaluation of detection determination of the number of sources and estimation performances of narrow band signal subspace processing for multiple source direction finding the probabilities of underestimating and overestimating the number of sources are derived under asymptotic conditions and around the threshold regions in terms of the choice of a penalty function and signal noise and array parameters for the cases of at most two closely spaced sources in the spatially white noise a scalar measure is introduced for the evaluation of the quality of the estimated signal subspace based on the statistics of this measure performance thresholds are demonstrated for the signal to noise ratio angle separation and correlation between two equipowered sources

local equivalence of symmetric hypersurfaces in s 2 x r and h 2 x r the chern moser normal form and its analog on finite type hypersurfaces in general do not respect symmetries extending the work of n k stanton we consider the local equivalence problem for symmetric levi degenerate hypersurfaces of finite type in mathbb c 2 the results give complete normalizations for such hypersurfaces which respect the symmetries in particular they apply to tubes and rigid hypersurfaces providing an effective classification the main tool is a complete normal form constructed for a general hypersurface with a tube model as an application we describe all biholomorphic maps between tubes answering a question posed by n hanges similar results for hypersurfaces admitting nontransversal symmetries are obtained

a fast thresholded landweber algorithm for wavelet regularized multidimensional deconvolution we present a fast variational deconvolution algorithm that minimizes a quadratic data term subject to a regularization on the norm of the wavelet coefficients of the solution previously available methods have essentially consisted in alternating between a landweber iteration and a wavelet domain soft thresholding operation while having the advantage of simplicity they are known to converge slowly by expressing the cost functional in a shannon wavelet basis we are able to decompose the problem into a series of subband dependent minimizations in particular this allows for larger subband dependent step sizes and threshold levels than the previous method this improves the convergence properties of the algorithm significantly we demonstrate a speed up of one order of magnitude in practical situations this makes wavelet regularized deconvolution more widely accessible even for applications with a strong limitation on computational complexity we present promising results in 3 d deconvolution microscopy where the size of typical data sets does not permit more than a few tens of iterations

local holomorphic isometries of a modified projective space into a standard projective space rational conformal factors we consider local modifications omega n f omega d of the fubini study metric with associated 1 1 form omega n on an open subset omega subset mathbb c mathbb p n induced by a local holomorphic mapping f omega rightarrow mathbb p d our main result is that there are gaps in potential dimensions m such that the modification can be obtained as h omega m for some local holomorphic mapping h omega rightarrow mathbb c mathbb p m we also consider the case of rational conformal factors

worst case cramer rao bounds for parametric estimation of superimposed signals with applications the problem of parameter estimation of superimposed signals in white gaussian noise is considered the effect of the correlation structure of the signals on the cramer rao bounds is studied for both the single and multiple experiment cases the best and worst conditions are found using various criteria the results are applied to the example of parameter estimation of superimposed sinusoids or plane wave direction finding in white gaussian noise and best and worst conditions on the correlation structure and relative phase of the sinusoids are found this provides useful information on the limits of the resolvability of sinusoid signals in time series analysis or of plane waves in array processing the conditions are also useful for designing worst case simulation studies of estimation algorithms and for the design of minimax signal acquisition and estimation procedures as demonstrated by an example

on the c regularity of cr mappings of positive codimension abstract the present paper tackles the c regularity problem for cr maps h m m between c smooth cr submanifolds m m embedded in complex spaces of possibly different dimensions for real hypersurfaces m c n 1 and m c n 1 with n n 1 and m strongly pseudoconvex we prove that every cr transversal map of class c n n 1 that is nowhere c on some non empty open subset of m must send this open subset to the set of d angelo infinite points of m as a corollary we obtain that every cr transversal map h m m of class c n n 1 must be c smooth on a dense open subset of m when m is of d angelo finite type another consequence establishes the following boundary regularity result for proper holomorphic maps in positive codimension given c n 1 and c n 1 pseudoconvex domains with smooth boundaries and both of d angelo finite type n n 1 any proper holomorphic map h that extends c n n 1 smoothly up to must be c smooth on a dense open subset of more generally for cr submanifolds m and m of higher codimensions our main result describes the impact of the existence of a nowhere smooth cr map h m m on the cr geometry of m allowing to extend the previously mentioned results in the hypersurface case to any codimension as well as deriving a number of regularity results for cr maps with d angelo infinite type targets

fundamental limitations on the resolution of deterministic signals we exploit results from detection theory for deriving fundamental limitations on resolution the results are general and are not based on any specific resolution technique and therefore hold for any method and for any resolution success rate we show that for signals with additive white gaussian noise the resolution limit is approximated by a simple expression related to the signal to noise ratio the signal waveform and the resolution success rate as an example we discuss the resolution of two complex exponentials with closely spaced frequencies the theoretical result is compared with the empirical performance of model order selection methods such as the akaike information criterion and the minimum description length

embedding strictly pseudoconvex domains into balls every relatively compact strictly pseudocc nvex domain d with c2 boundary in a stein manifold can be embedded as a closed complex submanifold of a finite dimensional ball however for each n 2 there exist bounded strictly pseudoconvex domains d in cn with real analytic boundary such that no proper holomorphic map from d into any finite dimensional ball extends smoothly to d 0 introduction in this paper we study the representations of bounded strictly pseudoconvex domains d c cn if the boundary of d is of class ck k e 2 3 oo then by a theorem of fornaess 8 and khenkin 13 d can be mapped biholomorphically onto the intersection xn q of a bounded strictly convex domain q c cn with ck boundary and a closed complex submanifold x defirxed in a neighborhood of q in cn x intersecting the boundary of q transversally moreover the map f d x n q extends to a holomorphic map on a neighborhood of d the convex domain q depends on d hence a natural question is whether a similar result holds with q replaced by the unit ball b z z1l zn e cn z 2 e zjl2 n that intersects bbn transversally such that d is biholomorphically equivalent to xn e3ff this question has been mentioned by lempert 14 pinduk 20 bedford 2 and others our main result is that the answer to this question is negative in general if d is as above then every biholomorphism of d onto xne3n extends smoothly to d according to 3 however we will show that not all such domains d admit a proper holomorphic map into a finite dimensional ball that is smooth on d theorem 1 1 a similar local result was obtained independently by faran 7 we shall show that the answer to the question q is positive if we allow the intersections of complex submanifolds with strictly convex domains q c cn with real analytic boundaries theorem 1 2 thetheoremsoffornaess 8 andkhenkin 13 onlygiveanqwith smooth boundary received by the editors april 4t 1985 1980 mathematics subject classification primary 32h05 1research supported by a fellowship from the alfred p sloan foundation t 1986 american mathematical society 0002 9947 86 1 00 25 per page

statistical angular resolution limit for point sources we define a statistical angular resolution limit arl on resolving two closely spaced point sources in a 3 d reference frame using constraints on the probabilities of false alarm and detection for a hypothesis test the arl can be used as a performance measure for sensor arrays in localizing remote sources and is applicable to different measurement models and applications e g radar sonar or astronomy by considering the asymptotic performance of the generalized likelihood ratio test glrt we derive the analytical expression of the arl and show that it is proportional to the square root of the cramer rao bound crb on the angular source separation or asymptotically the lower bound on the mean square angular error msaecrb numerical examples illustrate that the proposed arl is practically computable and achievable with large data samples our analytical result can replace the commonly used ad hoc resolution limits in existing literature

symmetries in cr complexity theory abstract we introduce the hermitian invariant group f of a proper rational map f between the unit ball in complex euclidean space and a generalized ball in a space of typically higher dimension we use properties of the groups to define the crucial new concepts of essential map and the source rank of a map we prove that every finite subgroup of the source automorphism group is the hermitian invariant group of some rational proper map between balls we prove that f is non compact if and only if f is a totally geodesic embedding we show that f contains an n torus if and only if f is equivalent to a monomial map we show that f contains a maximal compact subgroup if and only if f is equivalent to the juxtaposition of tensor powers we also establish a monotonicity result the group after intersecting with the unitary group does not decrease when a tensor product operation is applied to a polynomial proper map we give a necessary condition for f when the target is a generalized ball to contain automorphisms that move the origin

real hypersurfaces orders of contact and applications a fundamental problem in the modem theory of several complex variables concerns the boundary behavior of the cauchy riemann equations suppose that d is an open domain in cn and that its boundary m is a smooth real submanifold of cn how does the geometry of m influence the function theory on d one approach to this question is the a neumann problem 6 there one studies the inhomogeneous cauchy riemann equations au a where a is a 0 q form with distribution coefficients on the closed domain d u m satisfying the necessary compatibility condition a a 0 the a neumann problem constructs a particular solution u which is orthogonal to the null space of the complex laplacian kohn 10a has solved this problem and has shown that good local regularity properties for u in terms of a follow from so called subelliptic estimates it is natural to seek geometric conditions on m that are necessary and sufficient for these estimates in this paper we will be concerned with a certain geometric condition on m that we feel is the right one for subellipticity although the motivation for the questions discussed here comes from partial differential equations the techniques come from algebraic geometry to see why we state theorems of kohn greiner and catlin concerning subellipticity kohn 1oa has discovered a sufficient condition for a subelliptic estimate near a fixed point p in m in case d is pseudoconvex and is contained in c2 this condition is equivalent to the finiteness of order of tangency of every complex analytic one dimensional manifold with m at p greiner 13 established the necessity of this condition in

on the third gap for proper holomorphic maps between balls let f be a proper rational map from the complex ball mathbb b n into mathbb b n with n 7 and 3n 1 le n le 4n 7 then f is equivalent to a map g 0 dots 0 where g is a proper holomorphic map from mathbb b n into mathbb b 3n

strictly pseudoconvex domains in c n the theory which we have developed so far will be expanded in two ways 1 in this chapter we shall use the cauchy fantappie calculus to transform the bochner martinelli kernel into a kernel adapted to strictly pseudoconvex domains in n and prove a number of finiteness and vanishing theorems for these domains 2 in the next chapter we shall pass from n to arbitrary hermitian manifolds and establish the analogue of the bmk formula in that context obtaining along the way the hodge decomposition theorem on compact manifolds both lines of thought will merge in the subsequent chapters and lead to a solution of the levi problem and finiteness theorems for strictly pseudoconvex manifolds as well as to a solution of the overline partial neumann problem to be formulated later

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

estimating two dimensional frequencies by matrix enhancement and matrix pencil a new method called the matrix enhancement and matrix pencil memp method is presented for estimating two dimensional 2 d frequencies in the memp method an enhanced matrix is constructed from the data samples and then the matrix pencil approach is used to extract out the 2 d sinusoids from the principal eigenvectors of the enhanced matrix the memp method yields the estimates of the 2 d frequencies efficiently without solving the roots of a 2 d polynomial or searching in a 2 d space it is shown that the memp method can be faster than a 2 d fft method if the number of the 2 d sinusoids is much smaller than the data set simulation results are provided to show that the accuracy of the memp method can be very close to the cramer rao lower bound

boundary characterization of holomorphic isometric embeddings between indefinite hyperbolic spaces abstract we provide in this paper a boundary characterization in terms of the boundary cr invariants or pseudo hermitian invariants for holomorphic isometric embeddings between indefinite hyperbolic spaces of general codimensions

bianalytic maps between free spectrahedra linear matrix inequalities lmis i d sum j 1 g a jx j sum j 1 g a j x j succeq 0 play a role in many areas of applications the set of solutions of an lmi is a spectrahedron lmis in dimension free matrix variables model most problems in linear systems engineering and their solution sets are called free spectrahedra free spectrahedra are exactly the free semialgebraic convex sets this paper studies free analytic maps between free spectrahedra and under certain generically valid irreducibility assumptions classifies all those that are bianalytic the foundation of such maps turns out to be a very small class of birational maps we call convexotonic the convexotonic maps in g variables sit in correspondence with g dimensional algebras if two bounded free spectrahedra mathcal d a and mathcal d b meeting our irreducibility assumptions are free bianalytic with map denoted p then p must after possibly an affine linear transform extend to a convexotonic map corresponding to a g dimensional algebra spanned by u i a 1 ldots u i a g for some unitary u furthermore b and ua are unitarily equivalent the article also establishes a positivstellensatz for free analytic functions whose real part is positive semidefinite on a free spectrahedron and proves a representation for a free analytic map from mathcal d a to mathcal d b not necessarily bianalytic another result shows that a function analytic on any radial expansion of a free spectrahedron is approximable by polynomials uniformly on the spectrahedron these theorems are needed for classifying free bianalytic maps

rational proper holomorphic maps from b n into b 2 n in this paper we will investigate rational proper holomorphic maps from b n into b2 n when n 4

rigidity of proper holomorphic mappings between equidimensional hua domains hua domain named after chinese mathematician loo keng hua is defined as a domain in mathbb c n fibered over an irreducible bounded symmetric domain omega subset mathbb c d with the fiber over z in omega being a n d dimensional generalized complex ellipsoid sigma z in general a hua domain is a nonhomogeneous bounded pseudoconvex domain without smooth boundary the purpose of this paper is twofold firstly we obtain what seems to be the first rigidity results on proper holomorphic mappings between two equidimensional hua domains secondly we determine the explicit form of the biholomorphisms between two equidimensional hua domains as a special conclusion of this paper we completely describe the group of holomorphic automorphisms of the hua domain

extending proper holomorphic mappings of positive codimension in this paper we obtain results on holomorphic continuation of proper holomorphic mappings between pseudoconvex domains with real analytic boundaries in complex spaces of different dimensions equivalently we obtain results concerning the analyticity of cauchy riemann mappings between real analytic pseudoconvex hypersurfaces in complex spaces of different dimensions to begin with we recall the corresponding results for mappings of equidimensional domains let d and d be bounded pseudoconvex domains with smooth boundaries in c if the boundaries of d and d are strictly pseudoconvex or more generally of finite type in the sense of d angelo 15 then every proper holomorphic map of d onto d extends smoothly t o according to the results of bell and catlin 7 8 and diederich and forn ess 19 for mappings between strictly pseudoconvex domains this was proved by fefferman 26 and nirenberg webster and yang 37 if the boundaries of the pseudoconvex domains d d c c are real analytic then every proper holomorphic mapping of d onto d extends holomorphically to a neighborhood of 3 according to baouendi and rothschild 2 and diederich and forn ess 21 this reflection principle was first discovered by lewy 34 and pin6uk 38 for mappings between strictly pseudoconvex domains in the case of biholomorphic mappings between weakly pseudoconvex domains with realanalytic boundaries the result follows from the work of baouendi jacobowitz and treves 5 results in this direction were obtained in recent years by several authors see the papers 4 6 18 22 33 47 49 in this paper we are treating the case when the domains d and d have different dimensions to be specific we assume that d e c and d c c n are bounded pseudoconvex domains with real analytic boundaries and n n l in this situation a proper holomorphic map f d d need not be regular at the boundary for instance there exist proper holomorphic maps of balls of different dimensions

homotopy equivalence for proper holomorphic mappings abstract we introduce several homotopy equivalence relations for proper holomorphic mappings between balls we provide examples showing that the degree of a rational proper mapping between balls in positive codimension is not a homotopy invariant in domain dimension at least 2 we prove that the set of homotopy classes of rational proper mappings from a ball to a higher dimensional ball is finite by contrast when the target dimension is at least twice the domain dimension it is well known that there are uncountably many spherical equivalence classes we generalize this result by proving that an arbitrary homotopy of rational maps whose endpoints are spherically inequivalent must contain uncountably many spherically inequivalent maps we introduce whitney sequences a precise analogue in higher dimensions of the notion of finite blaschke product in one dimension we show that terms in a whitney sequence are homotopic to monomial mappings and we establish an additional result about the target dimensions of such homotopies

super rigidity for cr embeddings of real hypersurfaces into hyperquadrics we consider holomorphic mappings sending a given levi nondegenerate pseudoconcave hypersurface m in into a nondegenerate hyperquadric of the same signature in and show that if m is sufficiently close to a hyperquadric in a certain sense then any two such mappings differ only by an automorphism of the hyperquadric

maps from the two ball to the three ball in 4 webster proved the following theorem let b z e c 7 2 3 is a proper holomorphic map which is c a up to the boundary of b then f is linear fractional the purpose of this paper is to extend this result to the case n 2 however the theorem is false when n 2 f need not be linear fractional so instead of trying to prove this false theorem we shall instead try to make a list of maps f bz b a which are c 3 up to the boundary of course given such an f we can get another such by composing f with an automorphism of b 2 and an automorphism of b a so we make the

two dimensional modal analysis based on maximum likelihood the authors present a method for estimating the parameters of 2 d damped harmonic modal signals in additive gaussian noise this method applies in the cases of single or multiexperiment data and incoherent or coherent signals both synthesis and analysis models for the data are developed central to these models are the signal and orthogonal subspaces under the assumption of distinct modes in one of the two dimensions there exists an invertible function between the parameters of these two subspaces this function can be used to express the optimization problem given by maximum likelihood in terms of the orthogonal subspace the resulting problem can be solved by any of several methods including total least squares and iterative quadratic maximum likelihood iqml

uniqueness of certain polynomials constant on a line abstract we study a question with connections to linear algebra real algebraic geometry combinatorics and complex analysis let p x y be a polynomial of degree d with n positive coefficients and no negative coefficients such that p 1 when x y 1 a sharp estimate d 2 n 3 is known in this paper we study the p for which equality holds we prove some new results about the form of these sharp polynomials using these new results and using two independent computational methods we give a complete classification of these polynomials up to d 17 the question is motivated by the problem of classification of cr maps between spheres in different dimensions