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Carleman’s Formulas in Complex Analysis

Theory and Applications

  • Lev Aizenberg

Part of the Mathematics and Its Applications book series (MAIA, volume 244)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Carleman Formulas in the Theory of Functions of One Complex Variable and their Generalizations

  3. Carleman Formulas in Multidimensional Complex Analysis

  4. First Applications

    1. Lev Aizenberg
      Pages 143-162
    2. Lev Aizenberg
      Pages 163-191
    3. Lev Aizenberg
      Pages 192-203
  5. Supplement to the English Edition

  6. Back Matter
    Pages 276-299

About this book

Introduction

Integral representations of holomorphic functions play an important part in the classical theory of functions of one complex variable and in multidimensional com­ plex analysis (in the later case, alongside with integration over the whole boundary aD of a domain D we frequently encounter integration over the Shilov boundary 5 = S(D)). They solve the classical problem of recovering at the points of a do­ main D a holomorphic function that is sufficiently well-behaved when approaching the boundary aD, from its values on aD or on S. Alongside with this classical problem, it is possible and natural to consider the following one: to recover the holomorphic function in D from its values on some set MeaD not containing S. Of course, M is to be a set of uniqueness for the class of holomorphic functions under consideration (for example, for the functions continuous in D or belonging to the Hardy class HP(D), p ~ 1).

Keywords

Complex analysis Mathematica Symbol signal processing

Authors and affiliations

  • Lev Aizenberg
    • 1
  1. 1.Department of Function TheoryInstitute of PhysicsKrasnoyarskSiberia

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