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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

Part of the Operator Theory: Advances and Applications book series (OT, volume 206)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Leonid Lerer, Vadim Olshevsky, Ilya Spitkovsky
    Pages ix-xxii
  3. Israel Gohberg, Georg Heinig
    Pages 1-6
  4. Israel Gohberg, Nahum Krupnik
    Pages 111-125
  5. Israel Gohberg, Nahum Krupnik
    Pages 127-133
  6. Israel Gohberg, Nahum Krupnik
    Pages 135-144
  7. Israel Gohberg, Nahum Krupnik
    Pages 157-184
  8. Israel Gohberg, Nahum Krupnik
    Pages 185-199
  9. Israel Gohberg, Nahum Krupnik
    Pages 201-211
  10. Israel Gohberg, Nahum Krupnik
    Pages 213-217

About this book

Introduction

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.

Keywords

Factor Finite Integral equation Singular integral Volume algorithms applied mathematics commutative property construction convolution kernel mathematics operator singular integral equation time

Editors and affiliations

  • Leonid Lerer
    • 1
  • Vadim Olshevsky
    • 2
  • Ilya M. Spitkovsky
    • 3
  1. 1.Department of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael
  2. 2.Department of MathematicsUniversity of ConnecticutStorrsUSA
  3. 3.Department of MathematicsCollege of William & MaryWilliamsburgUSA

Bibliographic information