clifford theory for cyclic quotient groups abstract we describe in detail the clifford theory for cyclic quotient groups we pay particular attention to the field of definition of the characters involved as well as their schur indices

a fast algorithm for apes and capon spectral estimation in this paper we derive a novel implementation of some very computationally demanding matched filter bank based spectral estimators namely the amplitude and phase estimator apes the amplitude spectrum capon asc estimator and the power spectrum capon psc estimator filter bank based spectral estimation methods that adopt data dependent filter banks can provide spectra characterized by a significantly improved resolution compared to classical approaches however the computational complexity of the currently available implementation algorithms is extremely high a novel technique is introduced that provides efficient algorithms for the computation of the apes asc and psc spectra the proposed method is based on suitable displacement representations of all pertinent data matrices that are subsequently utilized for the computation of the associated complex valued polynomials the computational complexity of the proposed algorithms is lower than all relevant existing methods

iaa spectral estimation fast implementation using the gohberg semencul factorization we consider fast implementations of the weighted least squares based iterative adaptive approach iaa for one dimensional 1 d and two dimensional 2 d spectral estimation of uniformly sampled data iaa is a robust user parameter free and nonparametric adaptive algorithm that can work with a single data sequence or snapshot compared to the conventional periodogram iaa can be used to significantly increase the resolution and suppress the sidelobe levels however due to its high computational complexity iaa can only be used in applications involving small sized data we present herein novel fast implementations of iaa using the gohberg semencul g s type factorization of the iaa covariance matrices by exploiting the toeplitz structure of the said matrices we are able to reduce the computational cost by at least two orders of magnitudes even for moderate data sizes

the schur indices of the irreducible characters of the special linear groups abstract we compute the schur indices of each irreducible character of sl n q the special linear group for all n 1 and for all q a power of a prime

conformal deformation to constant negative scalar curvature on noncompact riemannian manifolds si m g est une variete de riemann complete de courbure scalaire non positive s satisfaisant s x e 0 pour x m m 0 ou m 0 est un ensemble compact alors il y a une metrique conforme complete g de courbure scalaire s 1

jacobians with group actions and rational idempotents abstract the object of this paper is to prove some general results about rational idempotents for a finite group g and deduce from them geometric information about the components that appear in the decomposition of the jacobian variety of a curve with g action we give an algorithm to find explicit primitive rational idempotents for any g as well as for rational projectors invariant under any given subgroup these explicit constructions allow geometric descriptions of the factors appearing in the decomposition of a jacobian with group action from them we deduce the decomposition of any prym or jacobian variety of an intermediate cover in the case of a jacobian with g action in particular we give a necessary and sufficient condition for a prym variety of an intermediate cover to be such a factor

higher adeles and non abelian riemann roch abstract we show a riemann roch theorem for group ring bundles over an arithmetic surface this is expressed using the higher adeles of beilinson parshin and the tame symbol via a theory of adelic equivariant chow groups and chern classes the theorem is obtained by combining a group ring coefficient version of the local riemann roch formula as in kapranov vasserot with results on k groups of group rings and an explicit description of group ring bundles over p 1 our set up provides an extension of several aspects of the classical frohlich theory of the galois module structure of rings of integers of number fields to arithmetic surfaces

positive harmonic functions on complete manifolds of negative curvature this paper studies the interaction between the geometry of complete riemannian manifolds of negative curvature and some aspects of function theory on these spaces the study of harmonic functions on the unit disc provides a classical and beautiful example of this interaction we recall some aspects of this below there is a well known representation of positive harmonic functions on the unit disc u due to herglotz 13 in terms of positive borel measures tt on the circle s1

a large class of non constant mean curvature solutions of the einstein constraint equations on an asymptotically hyperbolic manifold we construct solutions of the constraint equation with non constant mean curvature on an asymptotically hyperbolic manifold by the conformal method our approach consists in decreasing a certain exponent appearing in the equations constructing solutions of these sub critical equations and then in letting the exponent tend to its true value we prove that the solutions of the sub critical equations remain bounded which yields solutions of the constraint equation unless a certain limit equation admits a non trivial solution finally we give conditions which ensure that the limit equation admits no non trivial solution

efficient least squares fir system identification if finite impulse response fir system identification is performed by minimizing the squared error between the measured system output and an estimate from an fir system output a set of least squares normal equations to be solved for the fir system coefficients is obtained if the assumed fir system is of duration m samples the usual solution for the m least squares simultaneous equations requires a number of computational operations proportional to m3and storage of normal equation coefficients proportional to m2 the set of normal equations has an underlying structure however that can be exploited to yield a solution with computational operations proportional to m2and storage proportional to m such an efficient algorithmic solution is presented here

boundary behaviors for liouville s equation in planar singular domains abstract we study asymptotic behaviors near the boundary of complete metrics of constant curvature in planar singular domains and establish an optimal estimate of these metrics by the corresponding metrics in tangent cones near isolated singular points on boundary the conformal structure plays an essential role

the wave group on asymptotically hyperbolic manifolds abstract we show that the wave group on asymptotically hyperbolic manifolds belongs to an appropriate class of fourier integral operators then we use now standard techniques to analyze its regularized trace we prove that as in the case of compact manifolds without boundary the singularities of the regularized wave trace are contained in the set of periods of closed geodesics we also obtain an asymptotic expansion for the trace at zero

a fast algorithm for maximum likelihood estimation of harmonic chirp parameters the analysis of approximately periodic signals is an important element in numerous applications one generalization of standard periodic signals often occurring in practice is harmonic chirp signals where the instantaneous frequency increases decreases linearly as a function of time a statistically efficient estimator for extracting the parameters of the harmonic chirp model in additive white gaussian noise is the maximum likelihood ml estimator which recently has been demonstrated to be robust to noise and accurate even when the model order is unknown the main drawback of the ml estimator is that only very computationally demanding algorithms for computing an estimate are known in this paper we give an algorithm for computing an estimate to the ml estimator for a number of candidate model orders with a much lower computational complexity than previously reported in the literature the lower computational complexity is achieved by exploiting recursive matrix structures including a block toeplitz plus hankel structure the fast fourier transform and using a two step approach composed of a grid and refinement step to reduce the number of required function evaluations the proposed algorithms are assessed via monte carlo and timing studies the timing studies show that the proposed algorithm is orders of magnitude faster than a recently proposed algorithm for practical sizes of the number of harmonics and the length of the signal

calculating clifford classes for characters containing a linear character once abstract given a finite group g a normal subgroup n of g and an irreducible character of g the clifford class of describes the clifford theory including schur indices of with respect to the normal subgroup n assume there is a subgroup u of n and a linear character of u with multiplicity 1 in the restriction of to u we describe a method to calculate the clifford class of in certain cases this method helps in particular in the calculation of the schur indices of the irreducible characters of the groups contained between the general linear and the special linear groups

meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature abstract we give a detailed description of the schwartz kernel of the resolvent of the laplacian on a certain class of complete riemannian manifolds with negative sectional curvature near infinity these manifolds have compactifications as c manifolds with boundary on which the metric is conformai to a c metric up to the boundary with conformal factor 2 where is a defining function for the boundary the modified resolvent r s 2 n 1 defined and analytic in r n is shown to extend to be meromorphic in the whole complex plane when s 2 is equal to the sectional curvature at infinity for hyperbolic spaces obtained as quotients hn 1 where is a discrete group of fractional linear transformations having a geometrically finite fundamental domain without cusps at infinity s is constant we then deduce from the existence of this meromorphic extension of the resolvent the existence of a similar extension for the eisenstein series the basic method used to produce a parametrix for the laplacian is part of a more general construction by g mendoza and the second author but since this is not yet available the present paper has been made essentially self contained

computationally efficient capon and apes based coherence spectrum estimation the coherence spectrum is of notable interest as a bivariate spectral measure in a variety of application and the topic has lately attracted interest with the recent formulation of several high resolution data adaptive estimators in this work we further this development with the presentation of computationally efficient implementations of the capon and apes based msc estimators the presented implementations furthers the recent development of exploiting the estimators inherently low displacement rank of the necessary products of toeplitz like matrices to include also the required cross correlation covariance matrices for the mentioned coherence algorithms numerical simulations together with theoretical complexity measures illustrate the performance of the proposed implementations

computationally efficient two dimensional capon spectrum analysis we present a computationally efficient algorithm for computing the 2 d capon 1969 spectral estimator the implementation is based on the fact that the 2 d data covariance matrix will have a toeplitz block toeplitz structure with the result that the inverse covariance matrix can be expressed in closed form by using a special case of the gohberg heinig 1974 formula that is a function of strictly the forward 2 d prediction matrix polynomials furthermore we present a novel method based on a 2 d lattice algorithm to compute the needed forward prediction matrix polynomials and discuss the difference in the so obtained 2 d spectral estimate as compared with the one obtained by using the prediction matrix polynomials given by the whittle wiggins robinson 1963 1965 algorithm numerical simulations illustrate the improved resolution as well as the clear computational gain in comparison to both the well known classical implementation and the method published by liu et al see ieee trans aerosp electron syst vol 34 p 1314 19 1998

a fast algorithm for the inversion of block toeplitz matrices a technique to solve toeplitz matrices has been generalized to solve block toeplitz matrices this method is more efficient than the levinson recursion for moderately large matrix and block sizes this algorithm is in many cases preferable to cyclically preconditioned conjugate gradient algorithms

odd character correspondences in solvable groups abstract let g be a finite solvable group p be some prime let p be a sylow p subgroup of g and let n be its normalizer in g assume that n has odd order then we prove that there exists a bijection from the set of all irreducible characters of g of degree prime to p to the set of all the irreducible characters of degree prime to p of n such that it preserves the degree modulo p the field of values and the schur index over every field of characteristic zero this strengthens a more general recent result a turull character correspondences in solvable groups j algebra 295 2006 157 178 but only for the case under consideration here in addition we prove some other strong character correspondences that have very good rationality properties as one consequence we prove that a solvable group g has a non trivial rational irreducible character with degree prime to p if and only if the order of the normalizer of a sylow p subgroup of g has even order

strengthening the mckay conjecture to include local fields and local schur indices abstract a central problem in the representation theory of finite groups is given a prime p the study of relationships between the representations of g and those of p local subgroups of g the simplest of these is perhaps the mckay conjecture which concerns the number of irreducible characters of degree prime to p even though this conjecture remains open in an effort to understand it a number of strengthenings of it have been proposed recently isaacs and navarro and later navarro have proposed interesting stronger conjectures indicating that congruences modulo p of the degree of the characters and the invariance under certain type of fixed galois automorphism could be taken into account as well we propose an even further strengthening of mckay s conjecture which takes into account in addition the p local field of definition of the irreducible characters as well as their p local schur indices

clifford classes for some overgroups of the special linear groups abstract in a turull j algebra 235 2001 275 314 we calculated the schur index of each of the irreducible characters of the finite special linear groups in the present paper we calculate the schur index of all the irreducible characters of some overgroups of the special linear groups the overgroups in question are the special linear groups extended by diagonal automorphisms and the subgroups of the general linear group that contain the special linear group to each conjugacy class of irreducible characters of the special linear group in each overgroup is associated a clifford class the clifford class controls all the irreducible characters of the overgroup and intermediate subgroups that are related to the given irreducible by clifford theory knowing only the clifford class we can parametrize all the irreducible characters of the intermediate subgroups and compute for each parametrized irreducible character its field of character values as well as its schur index over each field we explicitly compute the clifford class in each case and deduce from it the information on the schur index of all the irreducible characters of the overgroups

fractional laplacian in conformal geometry abstract in this note we study the connection between the fractional laplacian operator that appeared in the recent work of caffarelli and silvestre and a class of conformally covariant operators in conformal geometry

superfast approximative implementation of the iaa spectral estimate in this correspondence we develop superfast approximative one dimensional algorithms for the computationally efficient implementation of the recent iterative adaptive approach iaa spectral estimate the proposed methods are based on rewriting the iaa algorithm with suitable gohberg semencul representations solving the resulting linear systems of equations using the preconditioned conjugate gradient method where a novel preconditioning is applied using an incomplete factorization of the toeplitz matrix numerical simulations illustrate the efficiency of both the proposed preconditioning as well as the overall algorithm offering a computational reduction of up to two orders of magnitude as compared to our recently proposed efficient and exact iaa implementation

asymptotically flat initial data with prescribed regularity at infinity we prove the existence of a large class of asymptotically flat initial data with non vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space like infinity in terms of powers of a radial coordinate

gluing and wormholes for the einstein constraint equations we establish a general gluing theorem for constant mean curvature solutions of the vacuum einstein constraint equations this allows one to take connected sums of solutions or to glue a handle wormhole onto any given solution away from this handle region the initial data sets we produce can be made as close as desired to the original initial data sets these constructions can be made either when the initial manifold is compact or asymptotically euclidean or asymptotically hyperbolic with suitable corresponding conditions on the extrinsic curvature in the compact setting a mild nondegeneracy condition is required in the final section of the paper we list a number ways this construction may be used to produce new types of vacuum spacetimes

the dirichlet problem at infinity for a negatively curved manifold on considere une n variete de riemann complete m qui est connexe et simplement connexe et a des courbures sectionnelles k bornees par 2 constantes finies negatives on etudie l existence de fonctions harmoniques bornees non constantes pour ces varietes

the brauer clifford group abstract clifford theory provides well behaved character correspondences between different groups which have isomorphic quotients given one such quotient group we define the brauer clifford group we show that each character of the original groups gives rise to a specific element of the brauer clifford group when two characters of different groups yield the same element of the brauer clifford group we obtain a very well behaved character correspondence between the characters of the different groups which preserves not only induction restriction multiplicities but also fields of values for the corresponding characters and schur indices we also show that the brauer clifford group has a natural homomorphism into a brauer group the brauer clifford group can be thought of as a refinement of the previously introduced clifford classes

a non compactness result on the fractional yamabe problem in large dimensions abstract let x n 1 g be an n 1 dimensional asymptotically hyperbolic manifold with conformal infinity m n h the fractional yamabe problem addresses to solve p g h u c u n 2 n 2 u 0 on m where c r and p g h is the fractional conformal laplacian whose principal symbol is the laplace beltrami operator on m in this paper we construct a metric on the half space x r n 1 which is conformally equivalent to the unit ball for which the solution set of the fractional yamabe equation is non compact provided that n 24 for 0 and n 25 for 1 where 0 1 is a certain transition exponent the value of turns out to be approximately 0 940197

invariant surface area functionals and singular yamabe problem in 3 dimensional cr geometry abstract we express two cr invariant surface area elements in terms of quantities in pseudohermitian geometry we deduce the euler lagrange equations of the associated energy functionals many solutions are given and discussed in relation to the singular cr yamabe problem we show that one of the energy functionals appears as the coefficient up to a constant multiple of the log term in the associated volume renormalization

a formula for calculating some schur indices abstract we describe a method for calculating the schur indices of certain characters of finite groups this method helps in particular in the calculation of the schur indices of the irreducible characters of the special linear groups

efficient order recursive algorithms for multichannel least squares filtering four efficient order recursive algorithms for least squares ls multichannel fir filtering and multivariable system identification are developed the need for such algorithms arises when the system model assigns an unequal number of delay elements to each input channel all proposed schemes provide considerable improvements over overparametrization or the zero padding approach first a block structures algorithm is derived it operates on boxes or blocks whose dimensions successively increase until their size equals the number of input channels as a result it requires linear system solvers and matrix multiplications the second algorithm manages to get free of block operations by proper decomposition of each block step involved in the first method into a number of scalar steps equal to the size of the block the third and the fourth algorithms provide highly concurrent alternatives that reduce processing time by an order magnitude an illustrative example from multichannel autoregressive spectral estimation is supplied

displacement structure of generalized inverse matrices abstract it is shown that matrices with a uv displacement structure possess generalized inverses with a vu displacement structure estimations for the displacement rank of the generalized inverses are presented the results apply to matrices of toeplitz vandermonde and cauchy type and provide formulas for generalized inverses which are important for fast algorithms

on hyperboloidal cauchy data for vacuum einstein equations and obstructions to smoothness of scri the relationship between the geometric properties of hyperboloidal cauchy data for vacuum einstein equations at the conformal boundary of the initial data surface and between the space time geometry is analyzed in detail we prove that a necessary condition for existence of a smooth or a polyhomogeneous scri i e a scri around which the metric is expandable in terms ofr j log i r rather than in terms ofr j is the vanishing of the shear of the conformal boundary of the initial data surface we derive the boundary constraints which have to be satisfied by an initial data set for compatibility with friedrich s conformal framework we show that a sufficient condition for existence of a smooth scri not necessarily complete is the vanishing of the shear of the conformal boundary of the initial data surface and smoothness up to boundary of the conformally rescaled initial data we also show that the occurrence of some log terms in an asymptotic expansion at the conformal boundary of solutions of the constraint equations is related to the non vanishing of the weyl tensor at the conformal boundary

parseval relationship of nonuniform samples of one and two dimensional signals it is shown that the parseval s relationship is extendable to a general set of nonuniform samples of a bandlimited signal further extensions to 2d signals are also considered

on the regularity of solutions to the yamabe equation and the existence of smooth hyperboloidal initial data for einstein s field equations the regularity of the solutions to the yamabe problem is considered in the case of conformally compact manifolds and negative scalar curvature the existence of smooth hyperboloidal initial data for einstein s field equations is demonstrated

complete conformal metrics with negative scalar curvature in compact riemannian manifolds soit m g une variete de riemann compacte de dimension n 3 et soit une sous variete lisse fermee de dimension d alors il y a une metrique conforme complete sur m m a courbure scalaire negative constante si et seulement si d n 2 2

the schur index of projective characters of symmetric and alternating groups the present paper answers a natural question that arises when one sets side by side two major contributions of issai schur to the theory of group representations in a monumental paper 13 schur described the projective characters of the symmetric group sn and the alternating group an for all n he calculated the representation groups of sn and an for all n and calculated the character table of these representation groups thereby describing the projective characters of sn and an in another seminal paper 12 schur defined and studied what is now called the schur index if 4f is an irreducible character of some finite group g and k is a field of characteristic zero the schur index mk g of qf with respect to k is the least positive multiplicity of q in a character afforded by a kg module the question is what are the schur indices of the characters of the representation groups of sn and an we give here a rule that describes the schur index of every irreducible character of the representation groups of sn and an for all n a substantial amount of research has been devoted to the schur index efforts have been directed both to finding its general properties and to calculating it for important classes of examples for example benard 1 showed that the schur index of every character of the weyl groups of type e6 e7 and e8 is one in 2 feit gives short proofs for the calculation of the schur index for many specific groups including benard s weyl groups of type e6 e7 and e8 and the representation groups of the sporadic simple groups other authors have studied the schur index for groups of lie type see for example 4 or 10 various methods are available to give upper bounds for the schur indices but it is usually harder to find their value when they are larger than one hence for the groups of lie type one can show that their schur indices are at most two in many cases and at most one in some cases but the question of exactly for what characters it is one and for which it is two has not been consistently answered

efficient recursive in order least squares fir filtering and prediction this paper is concerned with the efficient determination of the optimum in the least squares sense fir filter on the basis of data samples of the input and desired response signals by procedures recursive in the filter order this situation typically arises when no a priori statistics are available and the system order is not known the general multiinput multioutput multichannel case is considered here and a fast algorithm is presented requiring for single channel signals approximately 2s 15m multiplications mps per order m s being the number of samples in the special case of linear prediction it calls for about s 12m mps hence it offers a computational reduction of 5m and 2m mps in comparison to the methods of marple 1 and morf et al 2 respectively additionally the proposed scheme is inherently symmetric and is suited very well to initialization of fast sequential algorithms as well as algorithms searching for the optimum lag filter

on the smoothness of the critical sets of the cylinder at spatial infinity in vacuum spacetimes we analyze the appearance of logarithmic terms at the critical sets of friedrich s cylinder representation of spatial infinity it is shown that if the radiation field vanishes at all orders at the critical sets no logarithmic terms are produced in the formal expansions conversely it is proved that under the additional hypothesis that the spacetime has constant adm mass aspect and vanishing dual adm mass aspect by which we mean the limit of the bondi dual mass aspect on to the critical set this condition is also necessary for a spacetime to admit a smooth conformal representation at the critical sets

rational representations and permutation representations of finite groups we investigate the question which mathbb q valued characters and characters of mathbb q representations of finite groups are mathbb z linear combinations of permutation characters this question is known to reduce to that for quasi elementary groups and we give a solution in that case as one of the applications we exhibit a family of simple groups with rational representations whose smallest multiple that is a permutation representation can be arbitrarily large

character correspondences in solvable groups let g be a finite solvable group p be some prime let p be a sylow p subgroup of g and let n be its normalizer in g it is known that the number of irreducible characters of g of degree prime to p equals the number of irreducible characters of n of degree prime to p let f be any field of characteristic zero such that if g n is even then f contains qp q 2 the intersection of the field of p adic numbers with the field of rational numbers extended by all roots of unity whose order is a power to two in this paper we show that there exists a bijection from the set of all irreducible characters of g of degree prime to p to the set of all the irreducible characters of degree prime to p of n such that it preserves the degrees modulo p all the field of values over f and the schur index over every field containing f

efficient implementation of iterative adaptive approach spectral estimation techniques this paper presents computationally efficient implementations for several recent algorithms based on the iterative adaptive approach iaa for uniformly sampled one and two dimensional data sets considering both the complete data case and the cases when the data sets are missing samples either lacking arbitrary locations or having gaps or periodically reoccurring gaps by exploiting the method s inherent low displacement rank together with the development of suitable gohberg semencul representations and the use of data dependent trigonometric polynomials the proposed implementations are shown to offer a reduction of the necessary computational complexity by at least one order of magnitude numerical simulations together with theoretical complexity measures illustrate the achieved performance gain

new levinson schur and lattice type algorithms for linear phase filtering the ls estimate of the impulse response of fir filters with linear phase is known to be given by a structured linear set of equations three new algorithms are presented for the efficient solution of such systems one is the unwindowed extension of a previously derived levinson type structurally symmetric algorithm the second is a novel exact least squares lattice algorithm for time recursive processing the third is a schur type structurally symmetric algorithm with high degree of parallelism the new structures have considerably lower computational complexity and more parsimonious parametrization compared to previously derived algorithms this is because in contrast to the previously derived algorithms the new algorithms are developed so as to respect the symmetry which is intrinsic in the linear phase problem

reply to comment on parseval relationship of nonuniform samples of one and two dimensional signals the author presents a reply to the paper by zhu and leung ieee trans signal processing vol 42 no 3 p 2183 1994 which commented on the paper by marvasti and liu ieee trans acoust speech signal processing vol 38 no 6 p 1061 3 1990 the present author discusses a typographical error in the paper by marvasti and liu it is concluded that the theorem proofs are still correct and the conclusion still valid

amplitude estimation of sinusoidal signals survey new results and an application this paper considers the problem of amplitude estimation of sinusoidal signals from observations corrupted by colored noise a relatively large number of amplitude estimators which encompass least squares ls and weighted least squares wls methods are described additionally filterbank approaches which are widely used for spectral analysis are extended to amplitude estimation more exactly we consider the matched filterbank mafi approach and show that by appropriately designing the prefilters the mafi approach to amplitude estimation includes the wls approach the amplitude estimation techniques discussed in this paper do not model the observation noise and yet they are all asymptotically statistically efficient it is however their different finite sample properties that are of particular interest to this study numerical examples are provided to illustrate the differences among the various amplitude estimators although amplitude estimation applications are numerous we focus herein on the problem of system identification using sinusoidal probing signals for which we provide a computationally simple and statistically accurate solution

schur indices and schur groups w x schur groups were introduced in 8 as a certain kind of smallest groups admitting characters with nontrivial schur index indeed every finite group g having an irreducible character x with m x 1 involves such schur groups they occur as terminal steps by repeated application of the brauer witt theorem over local fields of characteristic zero there is a connection with the schur subgroup s k of the brauer group br k of such a field k this s k has been studied in detail by w x w x yamada 12 and quite recently by adem and milgram 1 from the character theoretic point of view it appears to be of interest to give explicit generators for s k in terms of schur groups see section 6 in the course w x of this investigation the authors noticed that there must be a gap in 8 concerning the exceptional dyadic schur groups yielding nontrivial 2 lo cal index it turned out that the definition of the schur groups of type qd q was too restrictive the correct definition will be given in section 5 below we take the opportunity to discuss these terminal q reduc2 tions once again and the class of 2 groups involved theorem 4 and 5 the schur groups admit faithful irreducible characters which are induced from linear characters of cyclic normal subgroups for the sake of clarity we begin our present work by making some general comments on schur indices in group extensions this should be compared with turull w x 11 our approach is perhaps more elementary and we just demonstrate w x how to use the results on stable clifford theory 7 more details may be w x found in the recent thesis 5 of the first named author

a superfast method for solving toeplitz linear least squares problems in this paper we develop a superfast o m n log 2 m n complexity algorithm to solve a linear least squares problem with an m n toeplitz coefficient matrix the algorithm is based on the augmented matrix approach the augmented matrix is further extended to a block circulant matrix and dft is applied this leads to an equivalent tangential interpolation problem where the nodes are roots of unity this interpolation problem can be solved by a divide and conquer strategy in a superfast way to avoid breakdowns and to stabilize the algorithm pivoting is used and a technique is applied that selects difficult points and treats them separately the effectiveness of the approach is demonstrated by several numerical examples 2003 elsevier science inc all rights reserved

structured matrices and newton s iteration unified approach abstract recent progress in the study of structured matrices shows advantages of unifying the treatment of various classes of such matrices we recall some fundamental techniques for such a unification and then specify it in full details for newton s iteration which rapidly improves an initial approximation to the inverse matrix by performing two matrix multiplications per recursive step the iteration is particularly suitable for n n structured matrices represented with o n entries of their short generators rather than with their own n 2 entries based on such a representation matrix operations are performed much more rapidly and use much less memory space a major problem is to control the length of the generators which tends to grow quite rapidly in the iterative process two known methods solve this problem for toeplitz like and cauchy like matrices we extend both methods to a more general class of structured matrices and estimate the convergence rate as well as the computational complexity some novel techniques are introduced in this study in particular for the estimation of the norms of the inverse displacement operators

approximate subspace based iterative adaptive approach for fast two dimensional spectral estimation in this paper we devise a new approach for fast implementation of two dimensional 2 d iterative adaptive approach iaa using single or multiple snapshots our underlying idea is to apply the subspace methodology in this nonparametric technique by performing the iaa on the dominant singular vectors extracted from the singular value decomposition svd or higher order svd of the multidimensional observations in doing so 2 d iaa is approximately realized by multiple steps of 1 d iaa implying that computational attractiveness is achieved particularly for large data size number of grid points and or snapshot number algorithms based on matrix and tensor operations are developed and their implementation complexities are analyzed computer simulations are also included to compare the proposed approach with the state of the art techniques in terms of resolution probability spectral estimation performance and computational requirement

the hodge cohomology of a conformally compact metric on etudie le laplacien de hogde agissant sur des k formes differentielles pour une classe de varietes de riemann completes a courbure sectionnelle negative proche de l infini ces varietes ont des compactifications c sur lesquelles la metrique est conforme a une metrique lisse jusqu au bord avec un facteur conforme 2 une fonction definissante pour le bord

fast lcmv based methods for fundamental frequency estimation recently optimal linearly constrained minimum variance lcmv filtering methods have been applied to fundamental frequency estimation such estimators often yield preferable performance but suffer from being computationally cumbersome as the resulting cost functions are multimodal with narrow peaks and require matrix inversions for each point in the search grid in this paper we therefore consider fast implementations of lcmv based fundamental frequency estimators exploiting the estimators inherently low displacement rank of the used toeplitz like data covariance matrices using as such either the classic time domain averaging covariance matrix estimator or if aiming for an increased spectral resolution the covariance matrix resulting from the application of the recent iterative adaptive approach iaa the proposed exact implementations reduce the required computational complexity with several orders of magnitude but as we show further computational savings can be obtained by the adoption of an approximative iaa based data covariance matrix estimator reminiscent of the recently proposed quasi newton iaa technique furthermore it is shown how the considered pitch estimators can be efficiently updated when new observations become available the resulting time recursive updating can reduce the computational complexity even further the experimental results show that the performances of the proposed methods are comparable or better than that of other competing methods in terms of spectral resolution finally it is shown that the time recursive implementations are able to track pitch fluctuations of synthetic as well as real life signals

fast mlm power spectrum estimation from uniformly spaced correlations we derive a fast algorithm for calculating the capon maximum likelihood method mlm power spectrum estimate when given uniformly spaced samples of the correlation function this algorithm computes a weighted correlation of the predictor coefficients found by running levinson recursion the fourier transform of the result gives the mlm spectrum this approach also suggests an interesting new comparison between mlm and mem

involutions acting on representations for a group g with order 2 automorphism we consider irreducible representations v of g such that where is the contragredient representation of this isomorphism gives rise to a nondegenerate bilinear form on v which is invariant unique up to scalar and consequently is either symmetric or skew symmetric for such a representation we study the question of when this form is symmetric and when it is skew symmetric we begin with recalling a method of prasad 13 in the case that is trivial and g is a finite group of lie type we apply a theorem of klyachko to obtain results for all representations of many of the groups sl n fq improving the results of prasad which were for generic representations in section 3 we start by generalizing lemma 1 to the case of any order 2 automorphism in lemma 2 we are able to apply this to get another proof of a theorem of gow 5 for the group gl n fq and the transposeinverse automorphism and in section 4 we are also able to apply lemma 2 to distinguished representations and gelfand pairs in section 5 we find a generating set for a finite group g given that we know certain information about the representations of g satisfying finally in section 6 we turn to the case of a locally compact totally disconnected group we adapt the methods of section 2 along with approximation by compact open subgroups to obtain an equivalent result of theorem 4 of gow for gl n f where f is a nonarchimedean local field

displacement structure theory and applications in this survey paper we describe how strands of work that are important in two different fields matrix theory and complex function theory have come together in some work on fast computational algorithms for matrices with what we call displacement structure in particular a fast triangularization procedure can be developed for such matrices generalizing in a striking way an algorithm presented by schur 1917 j reine angew math 147 1917 pp 205 232 in a paper on checking when a power series is bounded in the unit disc this factorization algorithm has a surprisingly wide range of significant applications going far beyond numerical linear algebra we mention among others inverse scattering analytic and unconstrained rational interpolation theory digital filter design adaptive filtering and state space least squares estimation

constructing representations of the finite symplectic group sp 4 q abstract let g be a finite group and be an irreducible character we say that a subgroup h is a subgroup if the restriction h of to h has at least one linear constituent of multiplicity 1 not every pair g has a subgroup but subgroups can be found in many cases the existence of such subgroups is of interest for several reasons one being that knowledge of a subgroup enables us to give a simple construction of a matrix representation of g affording in this paper we show that when g sp 4 q where q is a power of an odd prime p and h is a sylow p subgroup of g then h is a subgroup for every irreducible character with one exception we also find a p subgroup which is a subgroup for the exceptional character

calculating initial data for the conformal einstein equations by pseudo spectral methods abstract we present a numerical scheme for determining hyperboloidal initial data sets for the conformal field equations by using pseudo spectral methods this problem is to split into two parts the first step is the determination of a suitable conformal factor which transforms from an initial data set in physical space time to a hyperboloidal hypersurface in the ambient conformal manifold this is achieved by solving the yamabe equation a nonlinear second order equation the second step is a division by the conformal factor of certain fields which vanish on i the zero set of the conformal factor the challenge there is to numerically obtain a smooth quotient both parts are treated by pseudo spectral methods the nonlinear equation is solved iteratively while the division problem is treated by transforming the problem to the coefficient space solving it there by the qr factorisation of a suitable matrix and then transforming back these hyperboloidal initial data can be used to generate general relativistic space times by evolution with the conformal field equations

performance analysis of forward backward matched filterbank spectral estimators the problem of complex spectral estimation is of great interest in many applications this paper studies the general class of the forward backward matched filterbank mafi spectral estimators including the widely used capon as well as the more recently introduced amplitude and phase estimation of a sinusoid apes methods in particular we show by means of a higher order expansion technique that the one dimensional 1 d capon estimator underestimates the true spectrum whereas the 1 d apes method is unbiased we also show that the bias of the forward backward capon is half that of the forward only capon to within a second order approximation furthermore we show that these results can be extended to the two dimensional 2 d capon and apes estimators numerical examples are also presented to demonstrate quantitatively the properties of and the relation between these mafi estimators

comment on parseval relationship of nonuniform samples of one and two dimensional signals for original article see marvasti and liu ieee trans acoust speech signal processing vol 38 no 6 p 1061 3 1993 in the original article the proof of 1 states that x sub lp t is the low pass filtered version of the nonuniform samples and can be obtained by the following interpolation x sub lp t spl int sub spl infin sup spl infin x t sub n sinc w t t sub n dt the present authors suggest that this equation is incorrect because the response of a linear system to an arbitrary input signal is the convolution of the input signal and the impulse response df the system according to the signal and system theory thus they give a revised version of x sub lp t

efficient algorithms for adaptive capon and apes spectral estimation in this paper fast algorithms for adaptive capon and amplitude and phase estimation apes methods for spectral analysis of time varying signals are derived fast stable nonrecursive formulae are derived based on time shifting properties of the pertinent variables as a consequence efficient frequency domain recursive least squares rls based as well as fast rls based algorithms for the adaptive estimation of the power spectra are developed stability issues of the frequency domain estimators are considered and stabilization procedures are proposed the computational complexity of the proposed algorithms is lower than relevant existing methods the performance of the proposed algorithms is demonstrated through extensive simulations

shifted tableaux and the projective representations of symmetric groups les groupes de representation de s n classes de conjugaison algebres de clifford et la representation spin de base produits induits pour des representations spin une application caracteristique pour des caracteres de spin tableaux decales et q fonctions de schur les caracteres de spin irreductibles de s n et a n une analogue decalee de la regle lr produits tensoriels interieurs

unipotent elements of finite groups of lie type and realization fields of their complex representations abstract let p be a prime this paper classifies finite connected reductive groups g in characteristic p with the property that all complex character values of g belong to an unramified above p extension of the field of rational numbers the main application of these results is to the problem of describing the irreducible complex or p adic representations of g that remain absolutely irreducible under the brauer reduction modulo p an efficient approach to solve this problem for p 3 has been developed in our paper proc london math soc 3 84 2002 439 together with proc london math soc 3 84 2002 439 theorem 1 9 of the paper solves this problem for many finite connected reductive groups in characteristic p 3 additionally we show that all complex representations of any finite connected reductive group with no composition factor of type e7 2f e8 2f and e8 5f can be realized over a quadratic extension of an unramified above p extension of q

the dirichlet problem at infinity for manifolds of negative curvature on considere l existence de fonctions harmoniques bornees sur des varietes simplement connexes n n de courbure negative