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Integration on Infinite-Dimensional Surfaces and Its Applications

Overview

This book presents the theory of integration over surfaces in abstract topological vector space. Applications of the theory in different fields, such as infinite dimensional distributions and differential equations (including boundary value problems), shastic processes, approximation of functions, and calculus of variation on a Banach space, are treated in detail.
Audience: This book will be of interest to specialists in functional analysis, and those whose work involves measure...

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Paperback (Softcover reprint of hardcover 1st ed. 2000)
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Overview

This book presents the theory of integration over surfaces in abstract topological vector space. Applications of the theory in different fields, such as infinite dimensional distributions and differential equations (including boundary value problems), shastic processes, approximation of functions, and calculus of variation on a Banach space, are treated in detail.
Audience: This book will be of interest to specialists in functional analysis, and those whose work involves measure and integration, probability theory and shastic processes, partial differential equations and mathematical physics.

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Editorial Reviews

From the Publisher
'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 shastic processes.' Mathematical Reviews, 2001c
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Product Details

  • ISBN-13: 9789048153848
  • Publisher: Springer Netherlands
  • Publication date: 12/10/2010
  • Series: Mathematics and Its Applications (closed) Series , #496
  • Edition description: Softcover reprint of hardcover 1st ed. 2000
  • Edition number: 1
  • Pages: 272
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.60 (d)

Table of Contents

Preface. Introduction. Basic Notations. 1. Vector Measures and Integrals. 1.1. Definitions and Elementary Properties. 1.2. Principle of Boundedness. 1.3. Passage to the Limit Under Integral Sign. 1.4. Fubini's Theorem. 1.5. Reduction of a Vector Integral to a Scalar Integral. 2. Surface Integrals. 2.1. Smooth measures. 2.2. Definition of Surface Measures. The Invariance Theorem. 2.3. Elementary Properties of Surface Measures and Integrals. 2.4. Iterated Integration Formula. 2.5. Integration by Parts Formula. 2.6. Gauss-Ostrogradskii and Green's Formulas. 2.7. Vector Surface Measures. 2.8. A Case of the Banach Surfaces. 2.9. Some Special Surface Integrals. 3. Applications. 3.1. Distributions on a Hilbert Space. 3.2. Infinite-Dimensional Differential Equations. 3.3. Integral Representation of Functions on a Banach Space. Green's Measure. 3.4. On Parabolic and Elliptic Equations in a Space of Measures. 3.5. About the Amoothness of Distributions of Shastic Functionals. 3.6. Approximation of Functions of an Infinite-Dimensional Argument. 3.7. On a Differentiable Urysohn Function. 3.8. Calculus of Variations on a Banach Space. Comments. References. Index.

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