Integration on Infinite-Dimensional Surfaces and Its Applications / Edition 1

Integration on Infinite-Dimensional Surfaces and Its Applications / Edition 1

by A. Uglanov
     
 

This book presents the theory of integration over surfaces in abstract topological vector space. Applications of the theory in different fie lds, such as infinite dimensional distributions and differential equat ions (including boundary value problems), stochastic processes, approx imation of functions, and calculus of variation on a Banach space, are treated in

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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 fie lds, such as infinite dimensional distributions and differential equat ions (including boundary value problems), stochastic processes, approx imation of functions, and calculus of variation on a Banach space, are treated in detail.

Product Details

ISBN-13:
9780792361336
Publisher:
Springer Netherlands
Publication date:
01/31/2000
Series:
Mathematics and Its Applications (closed) Series, #496
Edition description:
2000
Pages:
272
Product dimensions:
0.75(w) x 6.14(h) x 9.21(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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