Coverart for item
The Resource Convolution equations and singular integral operators : selected papers of Israel Gohberg and Georg Heinig, Israel Gohberg and Nahum Krupnik, Leonid Lerer, Vadim Olshevsky, Ilya M. Spitkovsky, editors ; translated from the Russian by Oleksiy Karlovych

Convolution equations and singular integral operators : selected papers of Israel Gohberg and Georg Heinig, Israel Gohberg and Nahum Krupnik, Leonid Lerer, Vadim Olshevsky, Ilya M. Spitkovsky, editors ; translated from the Russian by Oleksiy Karlovych

Label
Convolution equations and singular integral operators : selected papers of Israel Gohberg and Georg Heinig, Israel Gohberg and Nahum Krupnik
Title
Convolution equations and singular integral operators
Title remainder
selected papers of Israel Gohberg and Georg Heinig, Israel Gohberg and Nahum Krupnik
Statement of responsibility
Leonid Lerer, Vadim Olshevsky, Ilya M. Spitkovsky, editors ; translated from the Russian by Oleksiy Karlovych
Contributor
Subject
Language
eng
Summary
  • This volume contains English translations of 13 groundbreaking papers on Toeplitz matrices and Wiener-Hopf equations and other classes of discrete and continuous convolution operators and singular integral equations. The papers are both of theoretical and numerical interest, in particular, they examine fast algorithms for inversion of these operators, the theory of discrete and continuous resultants, inversion via factorization, and symbol construction
  • The papers were originally written in Russian more than thirty years ago; their English translation is published here for the first time. These papers solved difficult problems and opened new venues in the above-mentioned areas. They are still frequently quoted, and moreover, they exert a continuing influence on numerical analysis and other areas of pure and applied mathematics and engineering. The book is addressed to a wide audience of mathematicians and engineers, from graduate students to researchers, whose interests lie in the above-mentioned areas --Book Jacket
Member of
Cataloging source
GW5XE
Dewey number
515.723
Index
no index present
Language note
Translated from the Russian
LC call number
QA321
LC item number
.G636 2010
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
  • 1961-
  • 1953-
http://library.link/vocab/relatedWorkOrContributorName
  • Lerer, Leonid
  • Olshevsky, Vadim
  • Spitkovskiĭ, Ilya M.
Series statement
Operator theory: advances and applications
Series volume
v. 206
http://library.link/vocab/subjectName
  • Convolutions (Mathematics)
  • Integral equations
  • Singular integrals
  • MATHEMATICS
  • Convolutions (Mathematics)
  • Integral equations
  • Singular integrals
  • Faltungsoperator
  • Singulärer Integraloperator
  • Toeplitz-Matrix
Label
Convolution equations and singular integral operators : selected papers of Israel Gohberg and Georg Heinig, Israel Gohberg and Nahum Krupnik, Leonid Lerer, Vadim Olshevsky, Ilya M. Spitkovsky, editors ; translated from the Russian by Oleksiy Karlovych
Instantiates
Publication
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Cover13; -- Table of Contents13; -- Preface -- Introduction -- References -- Inversion of Finite Toeplitz Matrices -- 1. Inversion of Toeplitz matrices -- 2. Inverse problem -- 3. Continual analogue -- References -- Inversion of Finite Toeplitz Matrices Consisting of Elements of a Noncommutative Algebra 13; -- 1. Theorems on inversion of Toeplitz matrices -- 2. Properties of solutions of equations -- 3. Inverse problem -- 4. Other theorems on inversion of Toeplitz matrices -- 5. Properties of solutions of equations -- 6. Inverse problem for equations -- References -- Matrix Integral Operators on a Finite Interval with Kernels Depending on the Difference of the Arguments13; -- 1. Two lemmas -- 2. The inversion formula -- 2.1. The main result of this section is the following. -- 2.2. Formula -- 3. Properties of the solutions of main equations -- 4. Inverse problem -- References -- The Resultant Matrix and its Generalizations. I. The Resultant Operator for Matrix Polynomials13; -- 1. Lemma on multiple extensions of systems of vectors -- 1.1. -- 1.2.13; -- 2. Auxiliary propositions -- 2.1. -- 2.2. -- 2.3. -- 3. Main theorem -- 3.1. -- 3.2. -- 3.3. -- 4. Applications -- 4.1. -- 4.2. -- 5. Kernel of Bezoutian -- 5.1. -- 5.2. -- References -- The Resultant Matrix and its Generalizations. II. The Continual Analogue of the Resultant Operator13; -- 1. Formulation of the main theorem -- 1.1. -- 1.2. -- 1.3. -- 1.4. -- 1.5. -- 2. A lemma -- 3. Proof of the main theorem -- 4. Scalar case -- 4.1. -- 4.2. -- 5. Applications -- 5.1. -- 5.2. -- 5.3. -- 6. Continual analogue of the Bezoutian -- References -- The Spectrum of Singular Integral Operators in Lp Spaces13; -- 1. The spectrum of discrete Wiener-Hopf equations in hp spaces -- 1.1. -- 1.2. -- 1.3. -- 2. The spectrum of singular integral operators in Lp spaces -- 3. Estimate for the norm of the singular integral operator -- 4. The spectrum of singular integral operators in symmetric spaces13; -- References -- On an Algebra Generated by the Toeplitz Matrices in the Spaces hp13; -- 1. Toeplitz operators in the spaces hp13; -- 1.1. -- 1.2. -- 2. Algebra generated by the Toeplitz operators -- 2.1. -- 2.2. -- References -- On Singular Integral Equations with Unbounded Coefficients13; -- 1. Auxiliary propositions -- 2. On the boundedness of the operator of singular integration -- 3. Operators of the form -- 4. Operators of the form -- References -- Singular Integral Equations with Continuous Coefficients on a Composed Contour13; -- 1. Auxiliary propositions and theorems on solvability13; -- 2. Quotient algebra -- 3. Normal solvability and index of operators in the algebra -- References -- On a Local Principle and Algebras Generated by Toeplitz Matrices13; -- 1. Localizing classes -- 1.1. -- 1.2. -- 1.3. -- 2. First example -- 2.1. -- 2.2. -- 3. Some properties of operators generated by Toeplitz matrices in lp spaces -- 3.1. -- 3.2. -- 3.3. -- 3.4. -- 4. Second example and its applications -- 4.1. -- 4.2. -- 5. Inversion of Toeplitz matrices -- 5.1. -- 5.2. -- 5.3. -- 6. Algebra of
Control code
710812494
Dimensions
unknown
Extent
1 online resource (xxii, 217 pages).
Form of item
online
Isbn
9783764389567
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
http://library.link/vocab/ext/overdrive/overdriveId
978-3-7643-8955-0
Specific material designation
remote
System control number
(OCoLC)710812494
Label
Convolution equations and singular integral operators : selected papers of Israel Gohberg and Georg Heinig, Israel Gohberg and Nahum Krupnik, Leonid Lerer, Vadim Olshevsky, Ilya M. Spitkovsky, editors ; translated from the Russian by Oleksiy Karlovych
Publication
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Cover13; -- Table of Contents13; -- Preface -- Introduction -- References -- Inversion of Finite Toeplitz Matrices -- 1. Inversion of Toeplitz matrices -- 2. Inverse problem -- 3. Continual analogue -- References -- Inversion of Finite Toeplitz Matrices Consisting of Elements of a Noncommutative Algebra 13; -- 1. Theorems on inversion of Toeplitz matrices -- 2. Properties of solutions of equations -- 3. Inverse problem -- 4. Other theorems on inversion of Toeplitz matrices -- 5. Properties of solutions of equations -- 6. Inverse problem for equations -- References -- Matrix Integral Operators on a Finite Interval with Kernels Depending on the Difference of the Arguments13; -- 1. Two lemmas -- 2. The inversion formula -- 2.1. The main result of this section is the following. -- 2.2. Formula -- 3. Properties of the solutions of main equations -- 4. Inverse problem -- References -- The Resultant Matrix and its Generalizations. I. The Resultant Operator for Matrix Polynomials13; -- 1. Lemma on multiple extensions of systems of vectors -- 1.1. -- 1.2.13; -- 2. Auxiliary propositions -- 2.1. -- 2.2. -- 2.3. -- 3. Main theorem -- 3.1. -- 3.2. -- 3.3. -- 4. Applications -- 4.1. -- 4.2. -- 5. Kernel of Bezoutian -- 5.1. -- 5.2. -- References -- The Resultant Matrix and its Generalizations. II. The Continual Analogue of the Resultant Operator13; -- 1. Formulation of the main theorem -- 1.1. -- 1.2. -- 1.3. -- 1.4. -- 1.5. -- 2. A lemma -- 3. Proof of the main theorem -- 4. Scalar case -- 4.1. -- 4.2. -- 5. Applications -- 5.1. -- 5.2. -- 5.3. -- 6. Continual analogue of the Bezoutian -- References -- The Spectrum of Singular Integral Operators in Lp Spaces13; -- 1. The spectrum of discrete Wiener-Hopf equations in hp spaces -- 1.1. -- 1.2. -- 1.3. -- 2. The spectrum of singular integral operators in Lp spaces -- 3. Estimate for the norm of the singular integral operator -- 4. The spectrum of singular integral operators in symmetric spaces13; -- References -- On an Algebra Generated by the Toeplitz Matrices in the Spaces hp13; -- 1. Toeplitz operators in the spaces hp13; -- 1.1. -- 1.2. -- 2. Algebra generated by the Toeplitz operators -- 2.1. -- 2.2. -- References -- On Singular Integral Equations with Unbounded Coefficients13; -- 1. Auxiliary propositions -- 2. On the boundedness of the operator of singular integration -- 3. Operators of the form -- 4. Operators of the form -- References -- Singular Integral Equations with Continuous Coefficients on a Composed Contour13; -- 1. Auxiliary propositions and theorems on solvability13; -- 2. Quotient algebra -- 3. Normal solvability and index of operators in the algebra -- References -- On a Local Principle and Algebras Generated by Toeplitz Matrices13; -- 1. Localizing classes -- 1.1. -- 1.2. -- 1.3. -- 2. First example -- 2.1. -- 2.2. -- 3. Some properties of operators generated by Toeplitz matrices in lp spaces -- 3.1. -- 3.2. -- 3.3. -- 3.4. -- 4. Second example and its applications -- 4.1. -- 4.2. -- 5. Inversion of Toeplitz matrices -- 5.1. -- 5.2. -- 5.3. -- 6. Algebra of
Control code
710812494
Dimensions
unknown
Extent
1 online resource (xxii, 217 pages).
Form of item
online
Isbn
9783764389567
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
http://library.link/vocab/ext/overdrive/overdriveId
978-3-7643-8955-0
Specific material designation
remote
System control number
(OCoLC)710812494

Library Locations

    • Ellis LibraryBorrow it
      1020 Lowry Street, Columbia, MO, 65201, US
      38.944491 -92.326012
Processing Feedback ...