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The Bochner-Martinelli Integral and Its Applications

  • Book
  • © 1995

Overview

Authors:
  1. Alexander M. Kytmanov

    1. Institute of Physics Akademgorodok, Krasnoyarsk State University, Krasnoyarsk, Russia

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-XI
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  2. The Bochner-Martinelli Integral

    • Alexander M. Kytmanov
    Pages 1-54

  3. CR-Functions Given on a Hypersurface

    • Alexander M. Kytmanov
    Pages 55-103

  4. Distributions Given on a Hypersurface

    • Alexander M. Kytmanov
    Pages 105-154

  5. The \(\bar \partial \)-Neumann Problem for Smooth Functions and Distributions

    • Alexander M. Kytmanov
    Pages 155-188

  6. Some Applications and Open Problems

    • Alexander M. Kytmanov
    Pages 189-232

  7. Holomorphic Extension of Functions into a Fixed Domain

    • Alexander M. Kytmanov
    Pages 233-270

  8. Back Matter

    Pages 271-305
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Keywords

About this book

The Bochner-Martinelli integral representation for holomorphic functions or'sev­ eral complex variables (which has already become classical) appeared in the works of Martinelli and Bochner at the beginning of the 1940's. It was the first essen­ tially multidimensional representation in which the integration takes place over the whole boundary of the domain. This integral representation has a universal 1 kernel (not depending on the form of the domain), like the Cauchy kernel in e . However, in en when n > 1, the Bochner-Martinelli kernel is harmonic, but not holomorphic. For a long time, this circumstance prevented the wide application of the Bochner-Martinelli integral in multidimensional complex analysis. Martinelli and Bochner used their representation to prove the theorem of Hartogs (Osgood­ Brown) on removability of compact singularities of holomorphic functions in en when n > 1. In the 1950's and 1960's, only isolated works appeared that studied the boundary behavior of Bochner-Martinelli (type) integrals by analogy with Cauchy (type) integrals. This study was based on the Bochner-Martinelli integral being the sum of a double-layer potential and the tangential derivative of a single-layer potential. Therefore the Bochner-Martinelli integral has a jump that agrees with the integrand, but it behaves like the Cauchy integral under approach to the boundary, that is, somewhat worse than the double-layer potential. Thus, the Bochner-Martinelli integral combines properties of the Cauchy integral and the double-layer potential.

Authors and Affiliations

  • Institute of Physics Akademgorodok, Krasnoyarsk State University, Krasnoyarsk, Russia

    Alexander M. Kytmanov

Bibliographic Information

  • Book Title: The Bochner-Martinelli Integral and Its Applications

  • Authors: Alexander M. Kytmanov

  • DOI: https://doi.org/10.1007/978-3-0348-9094-6

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag 1995

  • Softcover ISBN: 978-3-0348-9904-8Published: 08 October 2011

  • eBook ISBN: 978-3-0348-9094-6Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XII, 308

  • Topics: Analysis

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