Multidimensional Integral Representations

Problems of Analytic Continuation

Authors: Kytmanov, Alexander, Myslivets, Simona G.

  • 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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eBook $79.99
price for USA in USD (gross)
  • ISBN 978-3-319-21659-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.99
price for USA in USD
  • ISBN 978-3-319-21658-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.99
price for USA in USD
  • ISBN 978-3-319-37400-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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)


Table of contents (4 chapters)

  • Multidimensional Integral Representations

    Kytmanov, Alexander M. (et al.)

    Pages 1-19

  • Properties of the Bochner–Martinelli Integral and the Logarithmic Residue Formula

    Kytmanov, Alexander M. (et al.)

    Pages 21-74

  • On the Multidimensional Boundary Analogues of the Morera Theorem

    Kytmanov, Alexander M. (et al.)

    Pages 75-117

  • Functions with the One-Dimensional Holomorphic Extension Property

    Kytmanov, Alexander M. (et al.)

    Pages 119-217

Buy this book

eBook $79.99
price for USA in USD (gross)
  • ISBN 978-3-319-21659-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.99
price for USA in USD
  • ISBN 978-3-319-21658-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.99
price for USA in USD
  • ISBN 978-3-319-37400-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Multidimensional Integral Representations
Book Subtitle
Problems of Analytic Continuation
Authors
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-21659-1
DOI
10.1007/978-3-319-21659-1
Hardcover ISBN
978-3-319-21658-4
Softcover ISBN
978-3-319-37400-0
Edition Number
1
Number of Pages
XIII, 225
Topics