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Spectral Methods in Infinite-Dimensional Analysis

  • Y. M. Berezansky
  • Y. G. Kondratiev

Part of the Mathematical Physics and Applied Mathematics book series (MPAM, volume 12/1-2)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Y. M. Berezansky, Y. G. Kondratiev
    Pages 1-77
  3. Y. M. Berezansky, Y. G. Kondratiev
    Pages 79-258
  4. Y. M. Berezansky, Y. G. Kondratiev
    Pages 259-407
  5. Y. M. Berezansky, Y. G. Kondratiev
    Pages 409-521
  6. Y. M. Berezansky, Y. G. Kondratiev
    Pages 522-701
  7. Y. M. Berezansky, Y. G. Kondratiev
    Pages 702-819
  8. Back Matter
    Pages 891-949

About this book

Introduction

The Russian edition of this book appeared 5 years ago. Since that time, many results have been improved upon and new approaches to the problems investigated in the book have appeared. But the greatest surprise for us was to discover that there exists a large group of mathematicians working in the area of the so-called White Noise Analysis which is closely connected with the essential part of our book, namely, with the theory of generalized functions of infinitely many variables. The first papers dealing with White Noise Analysis were written by T. Hida in Japan in 1975. Later, this analysis was devel­ oped intensively in Japan, Germany, U.S.A., Taipei, and in other places. The related problems of infinite-dimensional analysis have been studied in Kiev since 1967, and the theory of generalized functions of infinitely many variables has been in­ vestigated since 1973. However, due to the political system in the U.S.S.R., contact be­ tween Ukrainian and foreign mathematicians was impossible for a long period of time. This is why, to our great regret, only at the end of 1988 did one of the authors meet L. Streit who told him about the existence of White Noise Analysis. And it become clear that many results in these two theories coincide and that, in fact, there exists a single theory and not two distinct ones.

Keywords

Potential STATISTICA Second quantization distribution harmonic analysis quantum field theory statistical physics

Authors and affiliations

  • Y. M. Berezansky
    • 1
  • Y. G. Kondratiev
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of ScienceKievUkraine

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-011-0509-5
  • Copyright Information Springer Science+Business Media B.V. 1995
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-4227-7
  • Online ISBN 978-94-011-0509-5
  • Buy this book on publisher's site