Yis ra ʿe l. Z. Gohberg Livres

This book is dedicated to a theory of traces and determinants on embedded algebras of linear operators, where the trace and determinant are extended from finite rank operators by a limit process. The self-contained material should appeal to a wide group of mathematicians and engineers, and is suitable for teaching.

The annotation covers various topics related to Nevanlinna-Pick interpolation for time-varying input-output maps in both discrete and continuous cases. It begins with an introduction and preliminaries, followed by discussions on J-unitary operators, generalized point evaluation, and bounded input-output maps. The text delves into the solution of the time-varying tangential interpolation problem, providing illustrative examples and references. Additionally, the work addresses the dichotomy of systems and the invertibility of linear ordinary differential operators, exploring their properties on both the real line and half line, as well as Fredholm properties and exponentially dichotomous operators. It further examines inertia theorems for block weighted shifts, detailing one-sided and two-sided systems, asymptotic inertia, and related references. The interpolation for upper triangular operators is also discussed, including colligations, characteristic functions, explicit formulas, admissibility, and various interpolation methods such as Nevanlinna-Pick and Carathéodory-Fejér interpolation, along with mixed interpolation problems and examples. Lastly, the text addresses minimality and realization of discrete time-varying systems, focusing on observability, reachability, proofs of minimality theorems, realizations of infinite lower triangular matrices, and systems with constant state space dimension, including periodical system

The book covers a range of advanced topics in mathematical analysis and operator theory. It begins with uncertainty principles related to time-frequency operators, followed by sampling results for time-frequency transformations and uncertainty principles for Gabor and wavelet frames. The exploration of matrix-valued continuous analogues of orthogonal polynomials includes preliminary results, the study of orthogonal operator-valued polynomials, and the distribution of zeros of matrix-valued Krein functions. The discussion on band extensions delves into the real line as a limit of discrete band extensions, introducing the entropy principle and outlining key preliminaries and main results. Further, it addresses weakly positive matrix measures and generalized Toeplitz forms, highlighting their lifting properties and applications to Hankel and Hilbert transform operators. The text also tackles the reduction of the abstract four block problem to a Nehari problem, presenting main theorems and their proofs. Additionally, it examines the state space method for integro-differential equations of Wiener-Hopf type with rational matrix symbols, including an introduction, main theorems, and detailed proofs. Lastly, it discusses symbols and asymptotic expansions across various contexts, including smooth and piecewise smooth symbols on Rn and T, as well as symbols discontinuous across hyperplanes. The program of the workshop is also includ

This monograph serves as the second volume of a graduate textbook on the modern theory of linear one-dimensional singular integral equations, which are increasingly significant due to their wide-ranging applications and the fact that they can often be solved explicitly. This volume builds upon material from the authors' earlier work published in 1973 and 1979, but it features numerous additions and complementary content that enhance its structure and accessibility for a broader audience. While the first volume focused on closed curves and continuous coefficients, this second volume addresses general curves and discontinuous coefficients. The text emphasizes key topics such as the invertibility and Fredholmness of singular integral operators, with a particular focus on inversion methods. The authors express gratitude to their editor, translator, and typist for their dedicated contributions to the project.

This volume features eight papers on recent advancements in interpolation theory for matrix functions and completion theory for matrices and operators. The first paper by D. Alpay and P. Loubaton examines a trigonometric moment problem for matrix-valued functions, emphasizing the realization approach in its resolution. The second paper by M. Bakonyi, V. G. Kaftal, G. Weiss, and H. J. Woerdeman addresses a matrix completion problem focusing on the lower triangular part of operator entries. It explores completions with both small usual and Hilbert-Schmidt norms, providing bounds for these norms and highlighting the significance of maximum entropy extensions, with applications to nest algebras and integral operators. The third paper by J. A. Ball, I. Gohberg, and M. A. Kaashoek presents solutions to time-varying interpolation problems, centering on the time-varying analog of the Nevanlinna-Pick tangential problem, where interpolation conditions arise from both sides. The state space theory of time-varying systems is crucial in this context. Together, these papers contribute to the understanding of complex matrix functions and operator theory.

This book is dedicated to the memory of an outstanding mathematician and personality, Vladimir Petrovich Potapov, who made important contributions to and exerted considerable influence in the areas of operator theory, complex analysis and their points of juncture. The book commences with insightful biographical material, and then presents a collection of papers on different aspects of operator theory and complex analysis covering those recent achievements of the Odessa-Kharkov school in which Potapov was very active. The papers deal with interrelated problems and methods. The main topics are the multiplicative structure of contractive matrix and operator functions, operators in spaces with indefinite scalar products, inverse problems for systems of differential equations, interpolation and approximation problems for operator and matrix functions. The book will appeal to a wide group of mathematicians and engineers, and much of the material can be used for advanced courses and seminars.

This book presents English translations of several influential papers on discrete and continuous convolution operators and singular integral operators originally published in Russian over thirty years ago. Despite their age, these works have proven to be significant in both pure and applied mathematics and engineering. The book is divided into two parts. The first part includes five papers by I. Gohberg and G. Heinig, focusing on the inversion of finite block Toeplitz matrices and their continuous counterparts, addressing both direct and inverse problems, as well as the theory of discrete and continuous resultants. The second part features eight papers by I. Gohberg and N. Krupnik, which explore one-dimensional singular integral operators with discontinuous coefficients across various spaces. Key topics include localization theory, the structure of the symbol, and equations with shifts. This compilation offers English-speaking readers a unique chance to engage with foundational work on Toeplitz matrices and singular integral operators, which are now regarded as classical. The translator and editors have corrected several misprints and minor inaccuracies during the preparation of the book, and special thanks are extended to A. Karlovich for his meticulous translation. This work serves as a tribute to the late Israel Gohberg, a remarkable mathematician.

Applications deal with interpolation, holomorphic families of subspaces and frames, holomorphic equivalence and diagonalization and Plemlj-Muschelishvili factorization Exposition of the material is made in style and terms which are used in Complex analysis of several variables Includes supplementary material: sn. pub/extras

This graduate text provides a careful treatment of the theory and applications of matrices in the presence of an indefinite inner product. The theory is a natural extension of the classical theory of hermitian and unitary matrices in linear algebra. Applications of the theory to differential equations, difference equations and systems theory are included. It is widely useful for engineers, scientists and mathematicians alike.

This volume is devoted to the life and work of the applied mathematician Professor Erhard Meister (1930-2001). He was a member of the editorial boards of this book series Operator The ory: Advances and Applications as well as of the journal Integral Equations and Operator Theory, both published by Birkhauser (now part of Springer-Verlag). Moreover he played a decisive role in the foundation of these two series by helping to establish contacts between Birkhauser and the founder and present chief editor of this book series after his emigration from Moldavia in 1974. The volume is divided into two parts. Part A contains reminiscences about the life of E. Meister including a short biography and an exposition of his professional work. Part B displays the wide range of his scientific interests through eighteen original papers contributed by authors with close scientific and personal relations to E. Meister. We hope that a great part of the numerous features of his life and work can be re-discovered from this book.