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Integration on Infinite-Dimensional Surfaces and Its Applications

  • Book
  • © 2000

Overview

Authors:
  1. A. V. Uglanov

    1. Yaroslavl State University, Yaroslavl, Russia

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Part of the book series: Mathematics and Its Applications (MAIA, volume 496)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • A. V. Uglanov
    Pages 1-8

  3. Basic Notations

    • A. V. Uglanov
    Pages 9-10

  4. Vector Measures and Integrals

    • A. V. Uglanov
    Pages 11-40

  5. Surface Integrals

    • A. V. Uglanov
    Pages 41-132

  6. Applications

    • A. V. Uglanov
    Pages 133-244

  7. Back Matter

    Pages 245-272
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Keywords

About this book

It seems hard to believe, but mathematicians were not interested in integration problems on infinite-dimensional nonlinear structures up to 70s of our century. At least the author is not aware of any publication concerning this theme, although as early as 1967 L. Gross mentioned that the analysis on infinite­ dimensional manifolds is a field of research with rather rich opportunities in his classical work [2. This prediction was brilliantly confirmed afterwards, but we shall return to this later on. In those days the integration theory in infinite­ dimensional linear spaces was essentially developed in the heuristic works of RP. Feynman [1], I. M. Gelfand, A. M. Yaglom [1]). The articles of J. Eells [1], J. Eells and K. D. Elworthy [1], H. -H. Kuo [1], V. Goodman [1], where the contraction of a Gaussian measure on a hypersurface, in particular, was built and the divergence theorem (the Gauss-Ostrogradskii formula) was proved, appeared only in the beginning of the 70s. In this case a Gaussian specificity was essential and it was even pointed out in a later monograph of H. -H. Kuo [3] that the surface measure for the non-Gaussian case construction problem is not simple and has not yet been solved. A. V. Skorokhod [1] and the author [6,10] offered different approaches to such a construction. Some other approaches were offered later by Yu. L. Daletskii and B. D. Maryanin [1], O. G. Smolyanov [6], N. V.

Reviews

`This book is highly recommended for every mathematician with an interest in recent developments in functional analysis, measure and integration, differential equations, approximations, calculus of variations and stochastic processes.' Mathematical Reviews, 2001c

Authors and Affiliations

  • Yaroslavl State University, Yaroslavl, Russia

    A. V. Uglanov

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