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Carleman’s Formulas in Complex Analysis

Theory and Applications

  • Book
  • © 1993

Overview

Authors:
  1. Lev Aizenberg

    1. Department of Function Theory, Institute of Physics, Krasnoyarsk, Siberia

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

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xx
    Download chapter PDF

  2. Carleman Formulas in the Theory of Functions of One Complex Variable and their Generalizations

    1. One-Dimensional Carleman Formulas

      • Lev Aizenberg
      Pages 1-17

    2. Generalization of One-Dimensional Carleman Formulas

      • Lev Aizenberg
      Pages 18-32

  4. First Applications

    1. Applications in Complex Analysis

      • Lev Aizenberg
      Pages 143-162

    2. Applications in Physics and Signal Processing

      • Lev Aizenberg
      Pages 163-191

    3. Computing Experiment

      • Lev Aizenberg
      Pages 192-203

  5. Supplement to the English Edition

    1. Criteria for Analytic Continuation. Harmonic Extension

      • Lev Aizenberg
      Pages 204-251

    2. Carleman Formulas and Related Problems

      • Lev Aizenberg
      Pages 252-275

  6. Back Matter

    Pages 276-299
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Keywords

About this book

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).

Authors and Affiliations

  • Department of Function Theory, Institute of Physics, Krasnoyarsk, Siberia

    Lev Aizenberg

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