Systems Approximation Singular Integral Operators And Related Topics

Author : Alexander A. Borichev,Nikolai K. Nikolski
Publisher : Birkhäuser
Page : 536 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783034883627

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Systems, Approximation, Singular Integral Operators, and Related Topics by Alexander A. Borichev,Nikolai K. Nikolski Pdf

This book is devoted to some topical problems and applications of operator theory and its interplay with modern complex analysis. It consists of 20 selected survey papers that represent updated (mainly plenary) addresses to the IWOTA 2000 conference held at Bordeaux from June 13 to 16, 2000. The main subjects of the volume include: - spectral analysis of periodic differential operators and delay equations, stabilizing controllers, Fourier multipliers; - multivariable operator theory, model theory, commutant lifting theorems, coisometric realizations; - Hankel operators and forms; - operator algebras; - the Bellman function approach in singular integrals and harmonic analysis, singular integral operators and integral representations; - approximation in holomorphic spaces. These subjects are unified by the common "operator theoretic approach" and the systematic use of modern function theory techniques.

Author : Alexander A. Borichev,Nikola©Œi Kapitonovich Nikol℗ʹski©Œi
Publisher : Birkhauser
Page : 527 pages
File Size : 55,6 Mb
Release : 2001-01-01
Category : Mathematics
ISBN : 0817666451

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Systems, Approximation, Singular Integral Operators, and Related Topics by Alexander A. Borichev,Nikola©Œi Kapitonovich Nikol℗ʹski©Œi Pdf

Author : Albrecht Böttcher,Marinus A. Kaashoek,Amarino Brites Lebre,Antonio, F. dos Santos,Frank-Olme Speck
Publisher : Springer Science & Business Media
Page : 412 pages
File Size : 52,8 Mb
Release : 2003-04-24
Category : Mathematics
ISBN : 3764369477

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Singular Integral Operators, Factorization and Applications by Albrecht Böttcher,Marinus A. Kaashoek,Amarino Brites Lebre,Antonio, F. dos Santos,Frank-Olme Speck Pdf

This volume contains the proceedings of the International Workshop on Operator Theory and Applications held at the University of Algarve in Faro, Portugal, September 12-15, in the year 2000. The main topics of the conference were !> Factorization Theory; !> Factorization and Integrable Systems; !> Operator Theoretical Methods in Diffraction Theory; !> Algebraic Techniques in Operator Theory; !> Applications to Mathematical Physics and Related Topics. A total of 94 colleagues from 21 countries participated in the conference. The major part of participants came from Portugal (32), Germany (17), Israel (6), Mexico (6), the Netherlands (5), USA (4) and Austria (4). The others were from Ukraine, Venezuela (3 each), Spain, Sweden (2 each), Algeria, Australia, Belorussia, France, Georgia, Italy, Japan, Kuwait, Russia and Turkey (one of each country). It was the 12th meeting in the framework of the IWOTA conferences which started in 1981 on an initiative of Professors 1. Gohberg (Tel Aviv) and J. W. Helton (San Diego). Up to now, it was the largest conference in the field of Operator Theory in Portugal.

Author : Leonid Lerer,Vadim Olshevsky,Ilya M. Spitkovsky
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 45,6 Mb
Release : 2011-02-03
Category : Mathematics
ISBN : 9783764389567

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Convolution Equations and Singular Integral Operators by Leonid Lerer,Vadim Olshevsky,Ilya M. Spitkovsky Pdf

This book consists of translations into English of several pioneering papers in the areas of discrete and continuous convolution operators and on the theory of singular integral operators published originally in Russian. The papers were wr- ten more than thirty years ago, but time showed their importance and growing in?uence in pure and applied mathematics and engineering. The book is divided into two parts. The ?rst ?ve papers, written by I. Gohberg and G. Heinig, form the ?rst part. They are related to the inversion of ?nite block Toeplitz matrices and their continuous analogs (direct and inverse problems) and the theory of discrete and continuous resultants. The second part consists of eight papers by I. Gohberg and N. Krupnik. They are devoted to the theory of one dimensional singular integral operators with discontinuous co- cients on various spaces. Special attention is paid to localization theory, structure of the symbol, and equations with shifts. ThisbookgivesanEnglishspeakingreaderauniqueopportunitytogetfam- iarized with groundbreaking work on the theory of Toepliz matrices and singular integral operators which by now have become classical. In the process of the preparation of the book the translator and the editors took care of several misprints and unessential misstatements. The editors would like to thank the translator A. Karlovich for the thorough job he has done. Our work on this book was started when Israel Gohberg was still alive. We see this book as our tribute to a great mathematician.

Author : Robert Ellis,Israel Gohberg
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 43,9 Mb
Release : 2003
Category : Mathematics
ISBN : 3764369299

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Orthogonal Systems and Convolution Operators by Robert Ellis,Israel Gohberg Pdf

The main concern of this book is the distribution of zeros of polynomials that are orthogonal on the unit circle with respect to an indefinite weighted scalar or inner product. The first theorem of this type, proved by M. G. Krein, was a far-reaching generalization of G. Szegö's result for the positive definite case. A continuous analogue of that theorem was proved by Krein and H. Langer. These results, as well as many generalizations and extensions, are thoroughly treated in this book. A unifying theme is the general problem of orthogonalization with invertible squares in modules over C*-algebras. Particular modules that are considered in detail include modules of matrices, matrix polynomials, matrix-valued functions, linear operators, and others. One of the central features of this book is the interplay between orthogonal polynomials and their generalizations on the one hand, and operator theory, especially the theory of Toeplitz marices and operators, and Fredholm and Wiener-Hopf operators, on the other hand. The book is of interest to both engineers and specialists in analysis.

Author : Daniel Alpay,Victor Vinnikov
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 54,8 Mb
Release : 2005-03-22
Category : Mathematics
ISBN : 3764372125

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Operator Theory, Systems Theory and Scattering Theory: Multidimensional Generalizations by Daniel Alpay,Victor Vinnikov Pdf

This volume contains a selection of papers, from experts in the area, on multidimensional operator theory. Topics considered include the non-commutative case, function theory in the polydisk, hyponormal operators, hyperanalytic functions, and holomorphic deformations of linear differential equations. Operator Theory, Systems Theory and Scattering Theory will be of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.

Author : Albrecht Böttcher,Yuri I. Karlovich,Ilya M. Spitkovsky
Publisher : Birkhäuser
Page : 464 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034881524

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Convolution Operators and Factorization of Almost Periodic Matrix Functions by Albrecht Böttcher,Yuri I. Karlovich,Ilya M. Spitkovsky Pdf

Many problems of the engineering sciences, physics, and mathematics lead to con volution equations and their various modifications. Convolution equations on a half-line can be studied by having recourse to the methods and results of the theory of Toeplitz and Wiener-Hopf operators. Convolutions by integrable kernels have continuous symbols and the Cauchy singular integral operator is the most prominent example of a convolution operator with a piecewise continuous symbol. The Fredholm theory of Toeplitz and Wiener-Hopf operators with continuous and piecewise continuous (matrix) symbols is well presented in a series of classical and recent monographs. Symbols beyond piecewise continuous symbols have discontinuities of oscillating type. Such symbols emerge very naturally. For example, difference operators are nothing but convolution operators with almost periodic symbols: the operator defined by (A

Author : Sergio Albeverio,Nils Elander,W. Nirrie Everitt,Pavel Kurasov
Publisher : Birkhäuser
Page : 423 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882194

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Operator Methods in Ordinary and Partial Differential Equations by Sergio Albeverio,Nils Elander,W. Nirrie Everitt,Pavel Kurasov Pdf

CO«i»b.H BaCHJIbeBHa lU>BaJIeBcR8JI (Sonja Kovalevsky) was born in Moscow in 1850 and died in Stockholm in 1891. Between these years, in the then changing and turbulent circumstances for Europe, lies the all too brief life of this remarkable woman. This life was lived out within the great European centers of power and learning in Russia, France, Germany, Switzerland, England and Sweden. To this day, now 150 years after her birth, her influence for and contribution to mathe matics, science, literature, women's rights and democratic government are recorded and reviewed, not only in Europe but now in countries far removed in time and distance from the lands of her birth and being. This volume, dedicated to her memory and to her achievements, records the Proceedings of the Marcus Wallenberg Symposium held, in memory of Sonja Kovalevsky, at Stockholm University from 18 to 22 June 2000. The symposium was held at the Department of Mathematics with its excellent library and lecture halls providing favourable working conditions. Within these pages are contained a curriculum vitae for Sonja Kovalevsky, a list of all her scientific publications, together with a copy of the moving and elegant obituary notice written by her friend and protector Gosta Mittag-Leffler. These papers are followed by a leading article entitled Sonja Kovalevsky: Her life and professorship in Stockholm, written especially for this volume by Jan-Erik Bjork in preparation for his major address to the Symposium.

Author : Genrich Belitskii,Vadim Tkachenko
Publisher : Birkhäuser
Page : 223 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880794

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One-dimensional Functional Equations by Genrich Belitskii,Vadim Tkachenko Pdf

The monograph is devoted to the study of functional equations with the transformed argument on the real line and on the unit circle. Such equations systematically arise in dynamical systems, differential equations, probabilities, singularities of smooth mappings, and other areas. The purpose of the book is to present modern methods and new results in the subject, with an emphasis on a connection between local and global solvability. The general concepts developed in the book are applicable to multidimensional functional equations. Some of the methods are presented for the first time in the monograph literature. The book is addressed to graduates and researchers interested in dynamical systems, differential equations, operator theory, or the theory of functions and their applications.

Author : Vladimir Ya. Eiderman,Mikhail V. Samokhin
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 43,9 Mb
Release : 2005-04-20
Category : Mathematics
ISBN : 3764372516

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Selected Topics in Complex Analysis by Vladimir Ya. Eiderman,Mikhail V. Samokhin Pdf

This volume opens with a paper by V.P. Havin that presents a comprehensive survey of the work of mathematician S.Ya. Khavinson. It includes a complete bibliography, previously unpublished, of 163 items, and twelve peer-reviewed research and expository papers by leading mathematicians, including the joint paper by Khavinson and T.S. Kuzina. The emphasis is on the usage of tools from functional analysis, potential theory, algebra, and topology.

Author : George A. Anastassiou
Publisher : Springer Science & Business Media
Page : 88 pages
File Size : 47,5 Mb
Release : 2011-07-25
Category : Mathematics
ISBN : 9781461405894

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Approximation by Multivariate Singular Integrals by George A. Anastassiou Pdf

Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly. This book studies the rate of convergence of these operators to the unit operator as well as the related simultaneous approximation. The last chapter, which includes many examples, presents a related Korovkin type approximation theorem for functions of two variables. Relevant background information and motivation is included in this exposition, and as a result this book can be used as supplementary text for several advanced courses. The results presented apply to many areas of pure and applied mathematics, such a mathematical analysis, probability, statistics and partial differential equations. This book is appropriate for researchers and selected seminars at the graduate level.

Author : Allan M. Krall
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 45,8 Mb
Release : 2002
Category : Mathematics
ISBN : 3764367016

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Hilbert Space, Boundary Value Problems, and Orthogonal Polynomials by Allan M. Krall Pdf

This monograph consists of three parts: - the abstract theory of Hilbert spaces, leading up to the spectral theory of unbounded self-adjoined operators; - the application to linear Hamiltonian systems, giving the details of the spectral resolution; - further applications such as to orthogonal polynomials and Sobolev differential operators. Written in textbook style this up-to-date volume is geared towards graduate and postgraduate students and researchers interested in boundary value problems of linear differential equations or in orthogonal polynomials.

Author : A. Böttcher,I. Gohberg
Publisher : Birkhäuser
Page : 325 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034890403

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Singular Integral Operators and Related Topics by A. Böttcher,I. Gohberg Pdf

This volume contains a selection of papers on modern operator theory and its applications, arising from a joint workshop on linear one-dimensional singular integral equations. The book is of interest to a wide audience in the mathematical and engineering sciences.

Author : Marinus A. Kaashoek,Sebastiano Seatzu,Cornelis van der Mee
Publisher : Springer Science & Business Media
Page : 478 pages
File Size : 45,7 Mb
Release : 2006-01-17
Category : Mathematics
ISBN : 9783764373986

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Recent Advances in Operator Theory and Its Applications by Marinus A. Kaashoek,Sebastiano Seatzu,Cornelis van der Mee Pdf

This book contains a selection of carefully refereed research papers, most of which were presented at the fourteenth International Workshop on Operator Theory and its Applications (IWOTA), held at Cagliari, Italy, from June 24-27, 2003. The papers, many of which have been written by leading experts in the field, concern a wide variety of topics in modern operator theory and applications, with emphasis on differential operators and numerical methods. The book will be of interest to a wide audience of pure and applied mathematicians and engineers.

Author : Daniel Alpay,Israel Gohberg
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 49,6 Mb
Release : 2006
Category : Language Arts & Disciplines
ISBN : 3764373709

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The State Space Method by Daniel Alpay,Israel Gohberg Pdf

The state space method developed in the last decades allows us to study the theory of linear systems by using tools from the theory of linear operators; conversely, it had a strong influence on operator theory introducing new questions and topics. The present volume contains a collection of essays representing some of the recent advances in the state space method. Methods covered include noncommutative systems theory, new aspects of the theory of discrete systems, discrete analogs of canonical systems, and new applications to the theory of Bezoutiants and convolution equations. The articles in the volume will be of interest to pure and applied mathematicians, electrical engineers and theoretical physicists.