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Author : S. G. Krein,E. M. Semenov
Publisher : American Mathematical Soc.
Page : 390 pages
File Size : 40,8 Mb
Release : 2002-10-21
Category : Mathematics
ISBN : 9780821831762
Author : I. Gohberg
Publisher : Birkhäuser
Page : 305 pages
File Size : 54,8 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783034877015
Author : I. Gohberg
Publisher : Birkhäuser
Page : 305 pages
File Size : 45,5 Mb
Release : 1990-10-01
Category : Science
ISBN : 3764325305
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, . . .
Author : Albrecht Pietsch
Publisher : Springer Science & Business Media
Page : 855 pages
File Size : 51,9 Mb
Release : 2007-12-31
Category : Mathematics
ISBN : 9780817645960
Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.
Author : Colin Bennett,Robert C. Sharpley
Publisher : Academic Press
Page : 489 pages
File Size : 40,7 Mb
Release : 1988-04-01
Category : Mathematics
ISBN : 9780080874487
This book presents interpolation theory from its classical roots beginning with Banach function spaces and equimeasurable rearrangements of functions, providing a thorough introduction to the theory of rearrangement-invariant Banach function spaces. At the same time, however, it clearly shows how the theory should be generalized in order to accommodate the more recent and powerful applications. Lebesgue, Lorentz, Zygmund, and Orlicz spaces receive detailed treatment, as do the classical interpolation theorems and their applications in harmonic analysis.The text includes a wide range of techniques and applications, and will serve as an amenable introduction and useful reference to the modern theory of interpolation of operators.
Author : I. Gohberg
Publisher : Birkhäuser
Page : 308 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034886154
Author : Jonathan R. Partington
Publisher : Cambridge University Press
Page : 184 pages
File Size : 55,6 Mb
Release : 2004-03-15
Category : Mathematics
ISBN : 0521546192
Publisher Description
Author : Hari Bercovic,Ciprian I. Foias
Publisher : Birkhäuser
Page : 311 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034884228
A collection of articles emphasizing modern interpolation theory, a topic which has seen much progress in recent years. These ideas and problems in operator theory, often arising from systems and control theories, bring the reader to the forefront of current research in this area.
Author : Cornelius Lanczos
Publisher : SIAM
Page : 579 pages
File Size : 46,6 Mb
Release : 1997-12-01
Category : Mathematics
ISBN : 9780898713701
A straightforward guide to numerical analysis, applied mathematics, or the solution procedures for differential equations.
Author : J. Bergh,J. Löfström
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642664519
The works of Jaak Peetre constitute the main body of this treatise. Important contributors are also J. L. Lions and A. P. Calderon, not to mention several others. We, the present authors, have thus merely compiled and explained the works of others (with the exception of a few minor contributions of our own). Let us mention the origin of this treatise. A couple of years ago, J. Peetre suggested to the second author, J. Lofstrom, writing a book on interpolation theory and he most generously put at Lofstrom's disposal an unfinished manu script, covering parts of Chapter 1-3 and 5 of this book. Subsequently, LOfstrom prepared a first rough, but relatively complete manuscript of lecture notes. This was then partly rewritten and thouroughly revised by the first author, J. Bergh, who also prepared the notes and comment and most of the exercises. Throughout the work, we have had the good fortune of enjoying Jaak Peetre's kind patronage and invaluable counsel. We want to express our deep gratitude to him. Thanks are also due to our colleagues for their support and help. Finally, we are sincerely grateful to Boe1 Engebrand, Lena Mattsson and Birgit Hoglund for their expert typing of our manuscript.
Author : J Szabados,P Vértesi
Publisher : World Scientific
Page : 320 pages
File Size : 45,6 Mb
Release : 1990-10-16
Category : Electronic
ISBN : 9789814507370
This book gives a systematic survey on the most significant results of interpolation theory in the last forty years. It deals with Lagrange interpolation including lower estimates, fine and rough theory, interpolatory proofs of Jackson and Teliakovski-Gopengauz theorems, Lebesgue function, Lebesgue constant of Lagrange interpolation, Bernstein and Erdös conjecture on the optimal nodes, the almost everywhere divergence of Lagrange interpolation for arbitrary system of nodes, Hermite-Fejer type and lacunary interpolation and other related topics. Contents:Lagrange InterpolationSome Convergent Interpolatory ProcessesThe Lebesgue Function and Lebesgue Function-Type SumsDivergence of Lagrange InterpolationHermite-Fejér and Hermite-Fejér Type InterpolationsComparison of Lagrange and Hermite-Fejér InterpolationsSome Problems in the Theory of Lacunary InterpolationMiscellaneous ProblemsSome Frequently Used Relation and Theorems Readership: Mathematicians. Keywords:Lagrange Interpolation;Divergence of the Interpolation;Lebesgue Function;Lebesgue Constant;Hermite-Fejer Interpolation;Convergent Interpolatory ProcessesReview:“… this is a very careful and exhaustive treatment of interpolation by univariate polynomials … It is the proverbial book nobody in the area can do without.”J Approximation Theory “… this is the first monograph devoted entirely to interpolation … As a whole this book can serve as an excellent and valuable deskcopy for researchers as well as for graduate students in approximation theory and related fields.”Acta Sci. Math. (Szeged)
Author : C. Foias,A.E. Frezho,I. Gohberg,M.A. Kaashoek
Publisher : Birkhäuser
Page : 587 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034887915
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. Initially the authors planned a number of papers treating nonstationary interpolation problems of Nevanlinna-Pick and Nehari type by reducing these nonstationary problems to stationary ones for operator-valued functions with operator arguments and using classical commutant lifting techniques. This reduction method required us to review and further develop the classical results for the stationary problems in this more general framework. Here the system theory turned out to be very useful for setting up the problems and for providing natural state space formulas for describing the solutions. In this way our work involved us in a much wider program than original planned. The final results of our efforts are presented here. The financial support in 1994 from the "NWO-stimulansprogramma" for the Thomas Stieltjes Institute for Mathematics in the Netherlands enabled us to start the research which lead to the present book. We also gratefully acknowledge the support from our home institutions: Indiana University at Bloomington, Purdue University at West Lafayette, Tel-Aviv University, and the Vrije Universiteit at Amsterdam. We warmly thank Dr. A.L. Sakhnovich for his carefully reading of a large part of the manuscript. Finally, Sharon Wise prepared very efficiently and with great care the troff file of this manuscript; we are grateful for her excellent typing.
Author : Grigore Arsene
Publisher : Birkhäuser
Page : 316 pages
File Size : 44,7 Mb
Release : 1984
Category : Juvenile Nonfiction
ISBN : UCAL:B4406632
Author : Avraham Feintuch,Israel Gohberg
Publisher : Springer Science & Business Media
Page : 448 pages
File Size : 49,5 Mb
Release : 1994
Category : Mathematics
ISBN : 3764350970
This volume presents the Proceedings of the Joint U.S. / Israel Workshop on Operator Theory and Its Applications, held February 24-28, 1992, at the Ben Gurion University of the Negev, Beersheva. This event was sponsored by the United States / Israel Binational Science Foundation and the Ben Gurion University of the Negev, and many outstanding experts in operator theory took part. The workshop honored Professor Emeritus Moshe Livsic on the occasion of his retirement. The volume contains a selection of papers covering a wide range of topics in modern operator theory and its applications, from abstract operator theory to system theory and computers in operator models. The papers treat linear and nonlinear problems, and study operators from different abstract and concrete classes. Many of the topics concern the area in which contributions of Moshe Livsic were extremely important. This book will appeal to a wide audience of pure and applied mathematicians and engineers.
Author : Israel Gohberg,Seymour Goldberg,Marinus Kaashoek
Publisher : Birkhäuser
Page : 428 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034879804
A comprehensive graduate textbook that introduces functional analysis with an emphasis on the theory of linear operators and its application to differential equations, integral equations, infinite systems of linear equations, approximation theory, and numerical analysis. As a textbook designed for senior undergraduate and graduate students, it begins with the geometry of Hilbert spaces and proceeds to the theory of linear operators on these spaces including Banach spaces. Presented as a natural continuation of linear algebra, the book provides a firm foundation in operator theory which is an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.
