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Orthogonal Systems and Convolution Operators

Author: Robert Ellis

Publisher: Springer Science & Business Media

Published: 2003

Total Pages: 264

ISBN-13: 9783764369293

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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.

Book Synopsis Orthogonal Systems and Convolution Operators by : Robert Ellis

Download or read book Orthogonal Systems and Convolution Operators written by Robert Ellis and published by Springer Science & Business Media. This book was released on 2003 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Orthogonal Systems and Convolution Operators

Author: Robert L. Ellis

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 244

ISBN-13: 3034880456

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In this book we study orthogonal polynomials and their generalizations in spaces with weighted inner products. The impetus for our research was a deep theorem due to M.G. Krein along with subsequent results of Krein and H. Langer. Together with our colleagues, we have worked in this area for nearly fifteen years, and the results of our research are presented here in unified form. We are grateful to the Department of mathematics at the University of Maryland in College Park and to Tel-Aviv University for their support and encouragement. The support of the Silver Family Foundation is also highly appreciated. Introduction The starting point ofthis book is a study ofthe orthogonal polynomials {qn In ?: O} obtained by orthogonalizing the power functions I, Z, z2, ... on the unit circle. The orthogonality is with respect to the scalar product defined by where the weight w is a positive integrable function on the unit circle. These ortho gonal polynomials are called the Szego polynomials associated with the weight w.

Book Synopsis Orthogonal Systems and Convolution Operators by : Robert L. Ellis

Download or read book Orthogonal Systems and Convolution Operators written by Robert L. Ellis and published by Birkhäuser. This book was released on 2012-12-06 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we study orthogonal polynomials and their generalizations in spaces with weighted inner products. The impetus for our research was a deep theorem due to M.G. Krein along with subsequent results of Krein and H. Langer. Together with our colleagues, we have worked in this area for nearly fifteen years, and the results of our research are presented here in unified form. We are grateful to the Department of mathematics at the University of Maryland in College Park and to Tel-Aviv University for their support and encouragement. The support of the Silver Family Foundation is also highly appreciated. Introduction The starting point ofthis book is a study ofthe orthogonal polynomials {qn In ?: O} obtained by orthogonalizing the power functions I, Z, z2, ... on the unit circle. The orthogonality is with respect to the scalar product defined by where the weight w is a positive integrable function on the unit circle. These ortho gonal polynomials are called the Szego polynomials associated with the weight w.

Factorization and Integrable Systems

Author: Israel Gohberg

Publisher: Springer Science & Business Media

Published: 2003-04-24

Total Pages: 234

ISBN-13: 9783764369385

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This volume comprises the specially prepared lecture notes of a a Summer School on "Factorization and Integrable Systems" held in September 2000 at the University of Algarve in Portugal. The main aim of the school was to review the modern factorization theory and its application to classical and quantum integrable systems. The program consisted of a number of short courses given by leading experts in the field.

Book Synopsis Factorization and Integrable Systems by : Israel Gohberg

Download or read book Factorization and Integrable Systems written by Israel Gohberg and published by Springer Science & Business Media. This book was released on 2003-04-24 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises the specially prepared lecture notes of a a Summer School on "Factorization and Integrable Systems" held in September 2000 at the University of Algarve in Portugal. The main aim of the school was to review the modern factorization theory and its application to classical and quantum integrable systems. The program consisted of a number of short courses given by leading experts in the field.

Advances in Pseudo-Differential Operators

Author: Ryuichi Ashino

Publisher: Springer Science & Business Media

Published: 2004-08-20

Total Pages: 252

ISBN-13: 9783764371401

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This volume consists of the plenary lectures and invited talks in the special session on pseudo-differential operators given at the Fourth Congress of the International Society for Analysis, Applications and Computation (ISAAC) held at York University in Toronto, August 11-16, 2003. The theme is to look at pseudo-differential operators in a very general sense and to report recent advances in a broad spectrum of topics, such as pde, quantization, filters and localization operators, modulation spaces, and numerical experiments in wavelet transforms and orthonormal wavelet bases.

Book Synopsis Advances in Pseudo-Differential Operators by : Ryuichi Ashino

Download or read book Advances in Pseudo-Differential Operators written by Ryuichi Ashino and published by Springer Science & Business Media. This book was released on 2004-08-20 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of the plenary lectures and invited talks in the special session on pseudo-differential operators given at the Fourth Congress of the International Society for Analysis, Applications and Computation (ISAAC) held at York University in Toronto, August 11-16, 2003. The theme is to look at pseudo-differential operators in a very general sense and to report recent advances in a broad spectrum of topics, such as pde, quantization, filters and localization operators, modulation spaces, and numerical experiments in wavelet transforms and orthonormal wavelet bases.

Spectral Methods for Operators of Mathematical Physics

Author: Jan Janas

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 247

ISBN-13: 3034879474

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This book presents recent results in the following areas: spectral analysis of one-dimensional Schrödinger and Jacobi operators, discrete WKB analysis of solutions of second order difference equations, and applications of functional models of non-selfadjoint operators. Several developments treated appear for the first time in a book. It is addressed to a wide group of specialists working in operator theory or mathematical physics.

Book Synopsis Spectral Methods for Operators of Mathematical Physics by : Jan Janas

Download or read book Spectral Methods for Operators of Mathematical Physics written by Jan Janas and published by Birkhäuser. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent results in the following areas: spectral analysis of one-dimensional Schrödinger and Jacobi operators, discrete WKB analysis of solutions of second order difference equations, and applications of functional models of non-selfadjoint operators. Several developments treated appear for the first time in a book. It is addressed to a wide group of specialists working in operator theory or mathematical physics.

Recent Advances in Operator Theory and Its Applications

Author: Marinus A. Kaashoek

Publisher: Springer Science & Business Media

Published: 2006-01-17

Total Pages: 480

ISBN-13: 3764373989

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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.

Book Synopsis Recent Advances in Operator Theory and Its Applications by : Marinus A. Kaashoek

Download or read book Recent Advances in Operator Theory and Its Applications written by Marinus A. Kaashoek and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Singular Integral Operators, Factorization and Applications

Author: Albrecht Böttcher

Publisher: Springer Science & Business Media

Published: 2003-04-24

Total Pages: 412

ISBN-13: 9783764369477

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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.

Book Synopsis Singular Integral Operators, Factorization and Applications by : Albrecht Böttcher

Download or read book Singular Integral Operators, Factorization and Applications written by Albrecht Böttcher and published by Springer Science & Business Media. This book was released on 2003-04-24 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Basic Classes of Linear Operators

Author: Israel Gohberg

Publisher: Springer Science & Business Media

Published: 2003-10-24

Total Pages: 448

ISBN-13: 9783764369309

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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.

Book Synopsis Basic Classes of Linear Operators by : Israel Gohberg

Download or read book Basic Classes of Linear Operators written by Israel Gohberg and published by Springer Science & Business Media. This book was released on 2003-10-24 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Operator Theoretical Methods and Applications to Mathematical Physics

Author: Israel Gohberg

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 472

ISBN-13: 3034879261

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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.

Book Synopsis Operator Theoretical Methods and Applications to Mathematical Physics by : Israel Gohberg

Download or read book Operator Theoretical Methods and Applications to Mathematical Physics written by Israel Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Selected Topics in Complex Analysis

Author: Vladimir Ya. Eiderman

Publisher: Springer Science & Business Media

Published: 2005-04-20

Total Pages: 240

ISBN-13: 9783764372514

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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.

Book Synopsis Selected Topics in Complex Analysis by : Vladimir Ya. Eiderman

Download or read book Selected Topics in Complex Analysis written by Vladimir Ya. Eiderman and published by Springer Science & Business Media. This book was released on 2005-04-20 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.