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Spectral Methods in Infinite-Dimensional Analysis

  • Book
  • © 1995

Overview

Authors:
  1. Y. M. Berezansky

    1. Institute of Mathematics, Ukrainian Academy of Science, Kiev, Ukraine

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  2. Y. G. Kondratiev

    1. Institute of Mathematics, Ukrainian Academy of Science, Kiev, Ukraine

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Rigged Spaces

    • Y. M. Berezansky, Y. G. Kondratiev
    Pages 1-77

  3. Generalized Functions of Infinitely Many Variables. Gaussian Measures

    • Y. M. Berezansky, Y. G. Kondratiev
    Pages 79-258

  4. Spectral Theorem

    • Y. M. Berezansky, Y. G. Kondratiev
    Pages 259-407

  5. Representations by Commuting Operators

    • Y. M. Berezansky, Y. G. Kondratiev
    Pages 409-521

  6. Application of the Theory of Expansions to Harmonic Analysis

    • Y. M. Berezansky, Y. G. Kondratiev
    Pages 522-701

  7. Infinite-Dimensional Elliptic Differential operators of the Second Order

    • Y. M. Berezansky, Y. G. Kondratiev
    Pages 702-819

  8. Infinite-Dimensional Differential Operators in the Models of Quantum Statistical Physics and Field Theory

    • Y. M. Berezansky, Y. G. Kondratiev
    Pages 820-890

  9. Back Matter

    Pages 891-949
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About this book

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.

Authors and Affiliations

  • Institute of Mathematics, Ukrainian Academy of Science, Kiev, Ukraine

    Y. M. Berezansky, Y. G. Kondratiev

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