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Multidimensional Integral Representations

Problems of Analytic Continuation

  • Book
  • © 2015

Overview

Authors:
  1. Alexander M. Kytmanov

    1. Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk, Russia

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  2. Simona G. Myslivets

    1. Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk, Russia

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Summarizes recent results on integral representations and residues
  • Includes studies on different families of complex lines and curves sufficient for holomorphic continuation of functions from the boundary of a bounded domain
  • Provides multidimensional logarithmic residue formulae with their boundary properties to obtain multidimensional boundary analogs of the Morera theorem

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Multidimensional Integral Representations

    • Alexander M. Kytmanov, Simona G. Myslivets
    Pages 1-19

  3. Properties of the Bochner–Martinelli Integral and the Logarithmic Residue Formula

    • Alexander M. Kytmanov, Simona G. Myslivets
    Pages 21-74

  4. On the Multidimensional Boundary Analogues of the Morera Theorem

    • Alexander M. Kytmanov, Simona G. Myslivets
    Pages 75-117

  5. Functions with the One-Dimensional Holomorphic Extension Property

    • Alexander M. Kytmanov, Simona G. Myslivets
    Pages 119-217

  6. Back Matter

    Pages 219-225
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Keywords

About this book

The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappiè, Koppelman, multidimensional logarithmic residue etc., and their boundary properties. The applications considered are problems of analytic continuation of functions from the boundary of a bounded domain in C^n. In contrast to the well-known Hartogs-Bochner theorem, this book investigates functions with the one-dimensional property of holomorphic extension along complex lines, and includes the problems of receiving multidimensional boundary analogs of the Morera theorem. This book is a valuable resource for specialists in complex analysis, theoretical physics, as well as graduate and postgraduate students with an understanding of standard university courses in complex, real and functional analysis, as well as algebra and geometry.

Reviews

“The monograph is essentially self-contained, requiring knowledge only of the contents of a basic course in several complex variables, this making it suitable for a graduate students seminar and independent study. The material is well organized and its presentation is lucid.” (Alekos Vidras, Mathematical Reviews, July, 2016)

“The monograph is based on recent results obtained by the authors. … The monograph will be useful to graduate students, PhD students, and researchers in function theory of several complex variables.” (Marek Jarnicki, zbMATH 1341.32001, 2016)

Authors and Affiliations

  • Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk, Russia

    Alexander M. Kytmanov, Simona G. Myslivets

Bibliographic Information

  • Book Title: Multidimensional Integral Representations

  • Book Subtitle: Problems of Analytic Continuation

  • Authors: Alexander M. Kytmanov, Simona G. Myslivets

  • DOI: https://doi.org/10.1007/978-3-319-21659-1

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Hardcover ISBN: 978-3-319-21658-4Published: 17 September 2015

  • Softcover ISBN: 978-3-319-37400-0Published: 22 October 2016

  • eBook ISBN: 978-3-319-21659-1Published: 09 September 2015

  • Edition Number: 1

  • Number of Pages: XIII, 225

  • Topics: Several Complex Variables and Analytic Spaces

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