Bücher von I. Gohberg

This paper is a largely expository account of the theory of p x p matrix polyno mials associated with Hermitian block Toeplitz matrices and some related problems of interpolation and extension. , hn of p x p matrices with h-i = hj for j = 0, ... We let k = O, ... , hk and shall denote its 1 inverse H k by (k)] k [ r = .. k = O, ...

If one assurnes that the function does not have a pole or a zero at infinity, the formula which solves this problem is (1) where Zl , " " Z/ are the given zeros with given multiplicates nl, " " n / and Wb" " W are the given p poles with given multiplicities ml, .

This book provides an introduction to the modern theory of polynomials whose coefficients are linear bounded operators in a Banach space - operator polynomials. Throughout many years, I have worked wtih several mathematicians on the subject of operator polynomials, and, consequently, their ideas have influenced my view of the subject;

This book is an introduction to the theory of linear one-dimensional singular integral equations. Singular integral equations have attracted more and more attention, because, on one hand, this class of equations appears in many applications and, on the other, it is one of a few classes of equations which can be solved in explicit form.

This book aims to present the theory of interpolation for rational matrix functions as a recently matured independent mathematical subject with its own problems, methods and applications.

The classicallossless inverse scattering (LIS) problem of network theory is to find all possible representations of a given Schur function s(z) (i. e. , a function which is analytic and contractive in the open unit disc D) in terms of an appropriately restricted class of linear fractional transformations. These linear fractional transformations corre­ spond to lossless, causal, time-invariant two port networks and from this point of view, s(z) may be interpreted as the input transfer function of such a network with a suitable load. More precisely, the sought for representation is of the form s(Z) = -{ -A(Z)SL(Z) + B(z)}{ -C(Z)SL(Z) + D(z)} -1 , (1. 1) where "the load" SL(Z) is again a Schur function and _ [A(Z) B(Z)] 0( ) (1. 2) Z - C(z) D(z) is a 2 x 2 J inner function with respect to the signature matrix This means that 0 is meromorphic in D and 0(z)* J0(z) ::5 J (1. 3) for every point zED at which 0 is analytic with equality at almost every point on the boundary Izi = 1. A more general formulation starts with an admissible matrix valued function X(z) = [a(z) b(z)] which is one with entries a(z) and b(z) which are analytic and bounded in D and in addition are subject to the constraint that, for every n, the n x n matrix with ij entry equal to X(Zi)J X(Zj )* i,j=l, . . .

This book presents a unified approach for solving both stationary and nonstationary interpolation problems, in finite or infinite dimensions, based on the commutant lifting theorem from operator theory and the state space method from mathematical system theory.

This monograph is the second volume of a graduate text book on the modern theory of linear one-dimensional singular integral equations. The authors Ramat-Aviv, Ramat-Gan, May 26, 1991 11 Introduction This book is the second volume of an introduction to the theory of linear one-dimensional singular integral operators.

This volume is dedicated to Tsuyoshi Ando, a foremost expert in operator theory, matrix theory, complex analysis, and their applications, on the occasion of his 60th birthday. This volume also contains papers on interpolation and completion problems, factorization problems and problems connected with complex analysis.

This book is an introduction to the theory of linear one-dimensional singular integral equations. Singular integral equations have attracted more and more attention, because, on one hand, this class of equations appears in many applications and, on the other, it is one of a few classes of equations which can be solved in explicit form.