a feynman kac ito formula for magnetic schrodinger operators on graphs in this paper we prove a feynman kac ito formula for magnetic schrodinger operators on arbitrary weighted graphs to do so we have to provide a natural and general framework both on the operator theoretic and the probabilistic side of the equation on the operator side we identify a very general class of potentials that allows the definition of magnetic schrodinger operators on the probabilistic side we introduce an appropriate notion of stochastic line integrals with respect to magnetic potentials apart from linking the world of discrete magnetic operators with the probabilistic world through the feynman kac ito formula the insights from this paper gained on both sides should be of an independent interest as applications of the feynman kac ito formula we prove a kato inequality a golden thompson inequality and an explicit representation of the quadratic form domains corresponding to a large class of potentials

kato class measures of symmetric markov processes under heat kernel estimates abstract we establish the coincidence of two classes of kato class measures in the framework of symmetric markov processes admitting upper and lower estimates of heat kernel under mild conditions one class of kato class measures is defined by way of the heat kernel another is defined in terms of the green kernel depending on some exponents related to the heat kernel estimates we also prove that p th integrable functions on balls with radius 1 having a uniformity of its norm with respect to centers are of kato class if p is greater than a constant related to the estimate under the same conditions these are complete extensions of some results for the brownian motion on euclidean space by aizenman and simon our result can be applicable to many examples for instance symmetric relativistic stable processes jump processes on d sets brownian motions on riemannian manifolds diffusions on fractals and so on

on conservation of probability and the feller property it is known that any smooth nondegenerate second order elliptic operator on a manifold dimension 2 has the form b where b is a vector field and is the laplace beltrami operator under some riemannian metric on the manifold in this paper we give several conditions on the ricci curvature ric s b associated with the operator b to ensure that the diffusion semigroup generated by b conserves probability and possesses the feller property

recent results for generalized exponential integrals abstract basic properties of the exponential integral function of real order ev x and relevant expressions for evaluating this special function are presented the mathematical results have been essentially obtained by generalizing known formulae valid for the usual exponential integral en x

semiclassical asymptotics gauge fields and quantum chaos a gauge field is given by a connection on a principal bundle p m we consider the semiclassical behavior of a family of schrodinger operators associated with a gauge field in the limit as h 0 we relate the spectral theory of such operators to behavior of the hamiltonian flow on the natural phase space associated to a gauge field examining in particular situations where this flow exhibits chaotic behavior

generalized inversion of block toeplitz matrices abstract an analog of a wiener hopf factorization method is proposed for finite block toeplitz matrices for an arbitrary rational matrix polynomial notions of essential indices and polynomials are introduced a connection between these notions and a wiener hopf factorization of some block triangular matrix functions is studied a formula for a generalized one sided two sided inversion of a block toeplitz matrix is found in terms of indices and essential polynomials of its symbol well known inversion formulas are obtained as special cases of this formula

on the partial realization problem abstract in this paper we take a unified approach to the partial realization problem in which we seek to incorporate ideas from numerical linear algebra most of which were originally developed in other contexts we approach the partial realization problem from several different angles and explore the connections to such topics as factoriza tion of hankel matrices block tridiagonalization generalizations of the lanczos process for biorthogonalization the euclidean algorithm and the principal part con tinued fractions of arne magnus the pade table and the berlekamp masseyalgo rithm in this way we are able to clarify some previous results by rissanen kalman and others and place them in a broader context this leads to several results and concepts which we think are new our analysis is restricted to the scalar case but some definitions and formulations have been rigged to facilitate an extension to the matrix case

path integrals and the essential self adjointness of differential operators on noncompact manifolds we consider schrodinger operators on possibly noncompact riemannian manifolds acting on sections in vector bundles with locally square integrable potentials whose negative part is in the underlying kato class using path integral methods we prove that under geodesic completeness these differential operators are essentially self adjoint on mathsf c infty 0 and that the corresponding operator closures are semibounded from below these results apply to nonrelativistic pauli dirac operators that describe the energy of hydrogen type atoms on riemannian 3 manifolds

stationary scattering in the semi classical limit for a schrodinger operator in a gauge field abstract we study the classical limit of the stationary scattering theory for a schrodinger operator in a compactly supported gauge field we show that under suitable hypotheses on the associated classical flow the scattering amplitude has a complete asymptotic expansion in the semi classical parameter and we determine the main term of this expansion

partial realization for singular systems in standard form abstract the partial realization problem under consideration consists in finding for a given sequence s s k 0 n 1 of blocks matrices a e b c of appropriate size such that s i ce n 1 i a i b and the identity matrix is a linear combination of a and e we discuss the question whether there is always a realization of this form for which the state space dimension is equal to the maximal rank of the underlying hankel matrices we show that this question has an affirmative answer if the block size is less than or equal to 2 and some other cases but not in general the paper strengthens results obtained by manthey et al cf w manthey u helmke d hinrichsen in u helmke et al eds operators systems and linear algebra teubner stuttgart 1997 pp 138 156 the main tools are the results of the authors obtained in connection with vandermonde factorization of block hankel matrices finally an interpretation of the problem in periodic discrete time systems is given

convergence of quantum systems on grids abstract we discuss here the convergence of quantum systems on grids embedded in r d and generalize the earlier results found for scalar valued potentials to the case of matrix valued potentials we also discuss the essential self adjointness of schrodinger operators for a large class of matrix potentials and give a feynman kac formula for their associated imaginary time schrodinger semigroups when the matrix potential is positive and continuous furthermore we establish an operator kernel estimate for the semigroups

the inverse eigenvalue problem for real symmetric toeplitz matrices we show that every set of n real numbers is the set of eigenvalues of an n x n real symmetric toeplitz matrix the matrix has a certain additional regularity the argument based on the topological degree is nonconstructive at t bell laboratories murray hill new jersey 07974 e mail address hjlfresearch att com this content downloaded from 157 55 39 29 on tue 12 apr 2016 08 53 54 utc all use subject to http about jstor org terms

the efficient computation of some generalised exponential integrals the accurate and efficient computation of the special functions gk x is discussed where gk x 1 k 1 1 exp xy log y k 1 dy y these functions appear in the computation of the derivatives of the l series of an elliptic curve and in radiative transfer problems from astrophysics by dividing 0 into 3 sub intervals we derive chebyshev polynomial expansions for gk k 1 4 with the coefficients given to an accuracy of 20 decimal places

fractional and wiener hopf factorizations abstract a connection between wiener hopf factorizations of an analytic matrix function a t and fractional factorizations of the rational part of a 1 t is obtained the result is applied to an explicit construction of wiener hopf factorizations of a t

small ħ asymptotics for quantum partition functions associated to particles in external yang mills potentials to a gauge field on a principalg bundlep m is associated a sequence of quantum mechanical hamiltonians as planck s constant 0 and a sequence of representations n ofg is taken this paper studies the associated quantum partition functions trace exp th n and produces a complete asymptotic expansion as 0 1 n of which the principal term proportional to the classical partition function is the familiar classical limit

approximation semi classique de l equation de heisenberg we study the semi classical approximation for the solution of heisenberg equation in terms of pseudo differential operators and establish a semi classical version of egorov s theorem as an application of these results we get the classical limit of quantum mechanical correlation functions for a class of non bounded observables

heat semigroup on a complete riemannian manifold let m be a complete riemannian manifold and p t x y the minimal heat kernel on m let p t be the associated semigroup we say that m is stochastically complete if int m p t x y dy 1 for all t 0 x in m we say that m has the c 0 diffusion property or the feller property if p tf vanishes at infinity for all t 0 whenever f is so let x 0 in m and let kappa r 2 geq inf ric x rho x x 0 leq r rho is the riemannian distance we prove that m is stochastically complete and has the c 0 diffusion property if int infty c kappa r 1 dr infty by studying the radial part of the riemannian brownian motion on m

heat equation derivative formulas for vector bundles we use martingale methods to give bismut type derivative formulas for differentials and co differentials of heat semigroups on forms and more generally for sections of vector bundles the formulas are mainly in terms of weitzenbock curvature terms in most cases derivatives of the curvature are not involved in particular our results improve b k driver s formula in 1997 j math pures appl 9 76 703 737 for logarithmic derivatives of the heat kernel measure on a riemannian manifold our formulas also include the formulas of k d elworthy and x m li 1998 c r acad sci paris ser i math 327 87 92

on generalized schrodinger semigroups abstract we prove a feynman kac formula for schrodinger type operators on vector bundles over arbitrary riemannian manifolds where the potentials are allowed to have strong singularities like those that typically appear in atomic quantum mechanical problems this path integral formula is then used to prove several l p type results like bounds on the ground state energy and l 2 l p smoothing properties of the corresponding schrodinger semigroups as another main result we will prove that with a little control on the riemannian structure the latter semigroups are also l 2 bounded continuous smoothing for kato decomposable potentials

interlacement of the even and odd spectra of real symmetric toeplitz matrices it is shown that for every n the even and odd spectra of real symmetric toeplitz matrices tn tr s nr s 1 are interlaced if tr 1 0 cos r d r 0 1 2 where f is monotonic and nonconstant

hamiltonian square roots of skew hamiltonian matrices abstract we present a constructive existence proof that every real skew hamiltonian matrix w has a real hamiltonian square root the key step in this construction shows how one may bring any such w into a real quasi jordan canonical form via symplectic similarity we show further that every w has infinitely many real hamiltonian square roots and give a lower bound on the dimension of the set of all such square roots some extensions to complex matrices are also presented

on parametrizations for the minimal partial realization problem abstract the paper considers parametrizations for minimal partial realizations of a finite sequence of markov parameters first it is shown that all minimal partial realizations have the same set of input and output kronecker indices a parametrization is obtained formulated in terms of a minimal set of extension entries then an i o canonical form is used as a parametrization for the set of minimal partial realizations it is shown that this allows to define the invariants of the problem moreover the i o canonical form is shown to contain a set of parameters that can be chosen such that any minimal partial realization can be represented

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

generalized inverses of hankel and toeplitz mosaic matrices abstract hankel and toeplitz mosaic matrices are block matrices with hankel or toeplitz blocks respectively it is shown that hankel and toeplitz mosaic matrices possess reflexive generalized inverses which are bezoutians furthermore the bezoutian structure of the moore penrose and group inverses is investigated

a least squares approach to reduce stable discrete linear systems preserving their stability abstract a new stability preserving model reduction algorithm for discrete linear siso systems based on a least squares approach is proposed similar to the pade approximation an equation system for the markov parameters involving a high dimensional hankel matrix is considered it is proved that approximate solutions computed via the moore penrose pseudo inverse give rise to a stability preserving reduction scheme furthermore the proposed algorithm is compared to the balanced truncation method showing comparable performance of the reduced systems

similarity of block companion and block toeplitz matrices a block companion matrix over a field of characteristic 0 is similar to a unique block unit upper hessenberg toeplitz matrix the proof is based on identities of formal power series and matrix representations of the shift of a polynomial model

kernel structure of toeplitz plus hankel matrices abstract the structure of the kernel of block toeplitz plus hankel matrices r aj k bj k where aj and bj are the given p q blocks with entries from a given field is investigated it is shown that r corresponds to two systems of at most p q vector polynomials from which a basis of the kernel of r and all other toeplitz plus hankel matrices with the same parameters aj and bj can be built the main result is an analogue of a known kernel structure theorem for block toeplitz and block hankel matrices

the trace formula for vector bundles ii fedn x e i i j k is a tempered distributional function of t the classical trace formula says that the singular support of ii is contained in the length spectrum of x moreover under suitable hypotheses on geodesic flow the trace formula gives considerable information about the singularities in ii see dg and c there is a fairly straightforward and not terribly interesting generalization of the trace formula to vector bundles see for instance the introduction to dg we will be concerned in this article with a much more subtle generalization inspired by recent articles of hogreve potthoff and schrader hps and schrader and taylor st in communications in mathematical physics let g be a compact lie group and ir p x a principle g bundle with connection given a finite dimensional unitary representation p of g we will denote by ep the vector bundle over x associated with p and by dp the associated connection now consider a ladder pe e 1 2 of irreducible representations of g this means that the maximal weight of pe is e times the maximal weight of p for given e let afc e 1 2 o be the spectrum of the laplace operator on c epe ae d pedpe e

semiclassical spectra of gauge fields abstract we study the asymptotic behavior of the eigenvalues of the schrodinger operator with a vector potential on a compact manifold as planck s constant tends to zero we obtain estimates in terms of periodic trajectories of wong s flow which are uniform in the charge parameter

uniqueness properties of minimal partial realizations abstract we characterize quantities poles and pole chains of the transfer functions of the minimal partial realizations of a given sequence of matrices s s0 s1 sn 1 which are uniquely determined by s furthermore the set of all points at which the transfer functions of all minimal partial realizations are analytic is described

centro symmetric and centro skewsymmetric toeplitz matrices and bezoutians abstract it is shown how the property of a toeplitz matrix to be centro symmetric or centro skewsymmetric in particular symmetric or skewsymmetric is reflected in its fundamental system furthermore centro symmetric and centro skewsymmetric bezoutians are described finally the representation of inverses of symmetric and skewsymmetric toeplitz matrices by special fundamental equations is discussed

the asymptotic spectra of banded toeplitz and quasi toeplitz matrices toeplitz matrices occur in many mathematical as well as scientific and engineering investigations this paper considers the spectra of banded toeplitz and quasi toeplitz matrices with emphasis on n

eigenvalues and pseudo eigenvalues of toeplitz matrices the eigenvalues of a nonhermitian toeplitz matrix a are usually highly sensitive to perturbations having condition numbers that increase exponentially with the dimension n an equivalent statement is that the resolvent zz a of a toeplitz matrix may be much larger in norm than the eigenvalues alone would suggest exponentially large as a function of n even when z is far from the spectrum because of these facts the meaningfulness of the eigenvalues of nonhermitian toeplitz matrices for any but the most theoretical purposes should be considered suspect in many applications it is more meaningful to investigate the e pseudo eigenvalues the complex numbers z with ll zz a 11 l this paper analyzes the pseudospectra of toeplitz matrices and in particular relates them to the symbols of the matrices and thereby to the spectra of the associated toeplitz and laurent operators our results are reasonably complete in the triangular case and preliminary in the cases of nontriangular toeplitz matrices block toeplitz matrices and toeplitz like matrices with smoothly varying coefficients computed examples of pseudospectra are presented throughout and applications in numerical analysis are mentioned

functions with bounded variation on a class of riemannian manifolds with ricci curvature unbounded from below after establishing some new global facts like a measure theoretic structure theorem and a new invariant characterization of sobolev functions about complex valued functions with bounded variation on arbitrary noncompact riemannian manifolds we extend results of miranda the second author paronetto preunkert and of carbonaro mauceri on the heat semigroup characterization of the variation of mathsf l 1 functions to a class of riemannian manifolds with possibly unbounded from below ricci curvature

a canonical matrix continued fraction solution of the minimal partial realization problem abstract a canonical algorithm for minimal partial realization of mimo systems is given the paper starts from the work of dickinson et al and anderson et al but reformulates it in the style of antoulas so that the elements to construct a matrix continued fraction are obtained it gives a detailed explicit algorithm to compute a uniquely defined canonical form of this continued fraction a number of remarkable properties of this canonical form are proved an example is included

vandermonde factorization and canonical representations of block hankel matrices abstract we study to which extent well known facts concerning vandermonde factorization or canonical representation of scalar hankel matrices transfer to block hankel matrices with p q blocks it is shown that nonsingular block hankel matrices can be factored like in the scalar case into nonconfluent vandermonde matrices and that the theorem on full rank factorization of arbitrary hankel matrices transfers in a weak version to the 2 2 block case but not to larger block sizes in general the minimal rank of a vandermonde factorization both with finite nodes and affine is described in terms of the hankel matrix the main tools are realization partial realization and moebius transformations

kac regular sets and sobolev spaces in geometry probability and quantum physics let omega subset m be an open subset of a riemannian manifold m and let v m rightarrow mathbb r be a kato decomposable potential with w 1 2 0 m v the natural form domain of the schrodinger operator delta v in l 2 m in this paper we study systematically the following question under which assumption on omega is the statement begin aligned text for all f in w 1 2 0 m v text with f 0 text a e in m setminus omega text one has f omega in w 1 2 0 omega v end aligned true for every such v generalizing a classical result by herbst and zhao who treat the euclidean mathbb r m and v 0 we prove that without any further assumptions on v the above property is satisfied if omega is kac regular a probabilistic property which means that the first exit time of brownian motion on m from omega is equal to its first penetration time to m setminus omega in fact we treat more general covariant schrodinger operators acting on sections in metric vector bundles allowing new results concerning the harmonicity of dirac spinors on singular subsets finally we prove that locally lipschitz regular omega s are kac regular

numerical solution of the inverse eigenvalue problem for real symmetric toeplitz matrices h j landau has recently given a nonconstructive proof of an existence theorem for the inverse eigenvalue problem for real symmetric toeplitz rst matrices this paper presents a procedure for the numerical solution of this problem the procedure is based on an implementation of newton s method that exploits landau s theorem and other special spectral properties of rst matrices with this version of newton s method together with the strategy proposed for applying it the method appears to be globally convergent however this is not proved

perturbations of invariant subspaces of unreduced hessenberg matrices non structured perturbation of invariant subspaces of unreduced i e nonderogatory hessenberg matrices is considered some perturbation results for the generalized eigenvectors and the characteristic polynomial of unreduced upper hessenberg matrices are given two theorems are on the perturbation of invariant subspaces which are somewhat similar to the sin q theorems of davis and kahan apart from the residual which we do not have here dense perturbations of unreduced hessenberg matrices are also considered finally we prove an invariant subspace perturbation theorem for nonderogatory matrices

papr analysis as a ratio of two random variables application to multicarrier systems with low subcarriers number the distribution of the peak to average power ratio papr of multicarrier systems is studied in the context of signals featuring low subcarriers number considering the mean power of the signal as a random variable a general cumulative distribution function of the papr is suggested we show that the new formulation is valid not only for low subcarriers number but also for larger subcarriers number thus an asymptotic analysis using a large subcarriers number proves a perfect concordance between the suggested approach and the state of the art derivations only valid for large subcarriers number all the theoretical developments are supported through simulations and we discuss the case of oversampled signals as well

generalized cauchy vandermonde matrices abstract matrices of the form c v consisting of a generalized cauchy matrix and a generalized vandermonde matrix are considered using the displacement structure of these matrices inversion formulas and criteria are presented the interpretation of linear systems with such a coefficient matrix as tangential interpolation problems leads to the concept of fundamental matrix which is basic in this approach for fundamental matrices recursion formulas are established from them fast inversion algorithms emerge that work for arbitrary nonsingular matrices of this kind

kernel structure of block hankel and toeplitz matrices and partial realization abstract the kernel structure of block hankel and toeplitz matrices is studied this leads to the concept of a fundamental system which is basic in the theory and provides in particular a natural background for the partial realization problem

on the eigenstructure of toeplitz matrices in spite of the fact that toeplitz eigenvalue problems have important applications in signal processing relatively little is known about the eigenstructure of finite real symmetric toeplitz matrices in this paper we exhibit two facts about the toeplitz eigenstructure problem first we show that any reciprocal or anti reciprocal n vector is an eigenvector for at least an n 1 2 dimensional linear space of real symmetric n n toeplitz matrices the second result is the fact that every n n toeplitz matrix can be imbedded into an n 1 n 1 toeplitz matrix which has a repeated smallest eigenvalue

a feynman kac formula for the quantum heisenberg ferromagnet i this article continues the analysis of the first arcticle under the same title using methods of stochastic analysis we prove feynman kac formulas for the relevant heat kernels we also present classical limit theorems

on the eigenvalue problem for toeplitz band matrices abstract a formula is given for the characteristic polynomial of an n th order toeplitz band matrix with bandwidth k n in terms of the zeros of a k th degree polynomial with coefficients independent of n the complexity of the formula depends on the bandwidth k and not on the order n also given is a formula for eigenvectors in terms of the same zeros and k coefficients which can be obtained by solving a k k homogeneous system

classical limits for quantum particles in external yang mills potentials we consider the limit 0 for nonrelativistic quantum particles moving in external yang mills potentials it is shown that the partition function and the solutions of the equations of motion converge to their corresponding classical counterparts

is every matrix similar to a toeplitz matrix abstract we show that every n n complex nonderogatory matrix is similar to a unique unit upper hessenberg toeplitz matrix the proof is constructive and can be adapted to nonderogatory matrices with entries in any field of characteristic zero or characteristic greater than n we also prove that every n n complex matrix with n 4 is similar to a toeplitz matrix

the radial part of brownian motion on a manifold a semimartingale property on montre que la discrepance entre les deux membres de la formule de ito forme un processus aleatoire monotone

gravity on finite groups gravity theories are constructed on finite groups g a self consistent review of the differential calculi on finite g is given with some new developments the example of a bicovariant differential calculus on the nonabelian finite group s3 is treated in detail and used to build a gravity like field theory on s3

inversion of mosaic hankel matrices via matrix polynomial systems abstract heinig and tewodors 18 give a set of components whose existence provides a necessary and sufficient condition for a mosaic hankel matrix to be nonsingular when this is the case they also give a formula for the inverse in terms of these components by converting these components into a matrix polynomial form we show that the invertibility conditions can be described in terms of matrix rational approximants for a matrix power series determined from the entries of the mosaic matrix in special cases these matrix rational approximations are closely related to pade and various well known matrix type pade approximants we also show that the inversion components can be described in terms of unimodular matrix polynomials these are shown to be closely related to the v and w matrices of antoulas used in his study of recursiveness in linear systems finally we present a recursion which allows for the efficient computation of the inversion components of all nonsingular principal mosaic hankel submatrices including the components for the matrix itself

an algebraic approach to the partial realization problem abstract the partial realization problem is treated algebraically using polynomial models the main idea is the kernels of certain projections of the hankel map which give rise to orthogonal direct sum decomposition of the state space minimality of partial realizations is based on minimal elements of these subspaces which arise as a natural consequence of the structural properties

on the evaluation of generalized exponential integrals e v x abstract in a previous paper we presented a method for evaluating the generalized exponential integral function ev x which is valid whenever x 0 and v 0 here we extend the evaluation of ev x to the whole domain x 0 r in the case x 1 we start from an initial value in the region of asymptotic calculation and then reach the required ev x making use of a suitable combination of taylor expansions and recurrences whenever 0 1 2 otherwise the evaluation method for ev x is mainly based on recursive calculations starting from a suitable initial element calculated by means of proper analytical expressions computational accuracy has been tested and some results of interest for applications are given

on recursiveness and related topics in linear systems a decomposition of matrix formal power series linear systems is developed the interconnections between formal power series realization pade approximation recursiveness berlekamp massey algorithm feedback interconnections matrix linear fractional representations matrix continued fractions and the matrix euclidean algorithm are thereby revealed

the generalized integro exponential function the generalized integro exponential function is defined in terms of the exponential integral incomplete gamma function and its derivatives with respect to order a compendium of analytic results is given in one section rational minimax approximations sufficient to permit the computation of the first six first order functions are reported in another section

a numerical method for generalized exponential integrals abstract we present a method for evaluation of the exponential integral e s x generalized to an arbitrary order s 0 the algorithm is valid whatever s 0 and x 0 in the region x 1 we start from a proper initial value obtained by asymptotic calculation and then compute the required e s x by means of a suitable combination of taylor s expansions and recurrences whatever s 0 when x s 0 x 0 s 0 1 which is obtained by the means of suitable expansions a forward recursion finally yields the required e s x numerical stability and accuracy of the proposed algorithm are discussed and some results given

multiplicative matrix valued functionals and the continuity properties of semigroups corresponding to partial differential operators with matrix valued coefficients abstract we define and examine certain matrix valued multiplicative functionals with local kato potential terms and use probabilistic techniques to prove that the semigroups of the corresponding self adjoint partial differential operators with matrix valued coefficients map from l 2 r n c d to the space of continuous bounded functions and that these semigroups have a jointly continuous and spatially bounded integral kernel these partial differential operators include yang mills type hamiltonians with electrical potentials that are elements of the matrix valued local kato class

the skew reflected gompertz distribution for analyzing symmetric and asymmetric data abstract in this work we have defined a new family of skew distribution the skew reflected gompertz we have also derived some of its probabilistic and inferential properties the maximum likelihood estimates of the proposed distribution parameters are obtained via an em algorithm and performances of the proposed model and its estimates are shown via simulation studies as well as real applications three real datasets are also used to illustrate the model performance which can compete against some well known skew distributions frequently used in applications

on the use of kernel structure for blind equalization the mathematical theory of kernel null space structure of hankel and hankel like matrices is applied to the problem of blind equalization of cochannel signals this approach provides a new perspective on the blind equalization problem and gives insights into the identifiability conditions already presented in the literature an algorithm is presented that tracks the exact null space of the symbol matrix even in the presence of noise this work exploits the shift structure in the oversampled channel output and the finite alphabet property of the signals previously these two properties were used independently in a two step equalize then separate process a contribution of the new approach is that is allows simultaneous exploitation of both the shift structure and the finite alphabet property of the signals

on minimality in the partial realization problem abstract a compression algorithm is constructed which allows one to reduce an arbitrary realization of a finite sequence of matrices m 1 m r to a minimal partial realization of m 1 m r furthermore a state space criterion of minimality of a partial realization and a formula for the minimal state space dimension are obtained

recursive relations for block hankel and toeplitz systems part ii dual recursions abstract the recursive relations given in part i of this report can be interpreted as recursions for the denominators of matrix pade approximants in this part we shall give dual relations for the corresponding numerators and residuals

not every matrix is similar to a toeplitz matrix abstract a negative answer to the question is every matrix similar to a toeplitz matrix raised by d s mackey n mackey and s petrovic linear algebra appl 297 1999 87 is given the tool of investigation is a result concerning the structure of the intersection of kernel and range of a toeplitz matrix which is of independent interest

concerning some integrals of the generalized exponential integral function abstract this paper deals with some integrals involving the generalized exponential integral e x which are of interest for applications new relations have been derived by generalizing known expressions valid for n integer numerical results are also given which extend existing tables to the entire real domain

on the geometry of semiclassical limits on dirichlet spaces abstract this paper is a contribution to semiclassical analysis for abstract schrodinger type operators on locally compact spaces let x be a metrizable separable locally compact space let be a radon measure on x with a full support let t x y p t x y be a strictly positive pointwise consistent heat kernel and assume that the generator h p 0 of the corresponding self adjoint contraction semigroup in l 2 x induces a regular dirichlet form then given a function 0 1 0 such that the limit lim t 0 p t x x t exists for all x x we prove that for every potential w x r one has lim t 0 t tr e t h p w e w x lim t 0 p t x x t d x for the schrodinger type operator h p w provided w satisfies very mild conditions at that are essentially only made to guarantee that the sum of quadratic forms h p w t is self adjoint and bounded from below for small t and to guarantee that e w x lim t 0 p t x x t d x the proof is probabilistic and relies on a principle of not feeling the boundary for p t x x in particular this result implies a new semiclassical limit result for partition functions valid on arbitrary connected geodesically complete riemannian manifolds and one also recovers a previously established semiclassical limit result for possibly locally infinite connected weighted graphs