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Harmonic Analysis and Boundary Value Problems in the Complex Domain

  • Book
  • © 1993

Overview

Authors:
  1. Mkhitar M. Djrbashian

    1. Academy of Sciences of Armenia, Institute of Mathematics, Yerevan, Armenia

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

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Preliminary results. Integral transforms in the complex domain

    • Mkhitar M. Djrbashian
    Pages 1-22

  3. Further results. Wiener-Paley type theorems

    • Mkhitar M. Djrbashian
    Pages 23-34

  4. Some estimates in Banach spaces of analytic functions

    • Mkhitar M. Djrbashian
    Pages 35-59

  5. Interpolation series expansions in spaces \( W_{1/2,\sigma }^{p,\omega } \) of entire functions

    • Mkhitar M. Djrbashian
    Pages 61-82

  6. Fourier type basic systems in L2(0, σ)

    • Mkhitar M. Djrbashian
    Pages 83-94

  7. Interpolation series expansions in spaces \( W_{s + 1/2,\sigma }^{p,w} \) of entire functions

    • Mkhitar M. Djrbashian
    Pages 95-120

  8. Basic Fourier type systems in L2 spaces of odd-dimensional vector functions

    • Mkhitar M. Djrbashian
    Pages 121-140

  9. Interpolation series expansions in spaces \( W_{s,\sigma }^{p,\omega }\) of entire functions

    • Mkhitar M. Djrbashian
    Pages 141-163

  10. Basic Fourier type systems in L2 spaces of even-dimensional vector functions

    • Mkhitar M. Djrbashian
    Pages 165-176

  11. The simplest Cauchy type problems and the boundary value problems connected with them

    • Mkhitar M. Djrbashian
    Pages 177-210

  12. Cauchy type problems and boundary value problems in the complex domain (the case of odd segments)

    • Mkhitar M. Djrbashian
    Pages 211-233

  13. Cauchy type problems and boundary value problems in the complex domain (the case of even segments)

    • Mkhitar M. Djrbashian
    Pages 235-251

  14. Back Matter

    Pages 253-258
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Keywords

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.

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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