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Birkhäuser

Harmonic Analysis and Boundary Value Problems in the Complex Domain

  • Book
  • © 1993

Overview

Part of the book series: Operator Theory: Advances and Applications (OT, volume 65)

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About this book

As is well known, the first decades of this century were a period of elaboration of new methods in complex analysis. This elaboration had, in particular, one char­ acteristic feature, consisting in the interfusion of some concepts and methods of harmonic and complex analyses. That interfusion turned out to have great advan­ tages and gave rise to a vast number of significant results, of which we want to mention especially the classical results on the theory of Fourier series in L2 ( -7r, 7r) and their continual analog - Plancherel's theorem on the Fourier transform in L2 ( -00, +00). We want to note also two important Wiener and Paley theorems on parametric integral representations of a subclass of entire functions of expo­ nential type in the Hardy space H2 over a half-plane. Being under the strong influence of these results, the author began in the fifties a series of investigations in the theory of integral representations of analytic and entire functions as well as in the theory of harmonic analysis in the com­ plex domain. These investigations were based on the remarkable properties of the asymptotics of the entire function (p, J1 > 0), which was introduced into mathematical analysis by Mittag-Leffler for the case J1 = 1. In the process of investigation, the scope of some classical results was essentially enlarged, and the results themselves were evaluated.

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Keywords

Table of contents (12 chapters)

Authors and Affiliations

  • Academy of Sciences of Armenia, Institute of Mathematics, Yerevan, Armenia

    Mkhitar M. Djrbashian

Bibliographic Information

  • Book Title: Harmonic Analysis and Boundary Value Problems in the Complex Domain

  • Authors: Mkhitar M. Djrbashian

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-8549-2

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1993

  • Hardcover ISBN: 978-3-7643-2855-9Published: 01 January 1993

  • Softcover ISBN: 978-3-0348-9674-0Published: 21 October 2012

  • eBook ISBN: 978-3-0348-8549-2Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XIII, 258

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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