Approximation Problems in Analysis and Probability

M.P. Heble (Eds.)0444880216, 9780444880215, 9780080872704

This is an exposition of some special results on analytic or C∞-approximation of functions in the strong sense, in finite- and infinite-dimensional spaces. It starts with H. Whitney’s theorem on strong approximation by analytic functions in finite-dimensional spaces and ends with some recent results by the author on strong C∞-approximation of functions defined in a separable Hilbert space. The volume also contains some special results on approximation of stochastic processes. The results explained in the book have been obtained over a span of nearly five decades.

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Table of contents :
Content:
Edited by
Pages ii-iii

Copyright page
Page iv

Dedication
Page v

Introduction
Pages ix-xi

Chapter I Weierstrass-Stone theorem and generalisations – a brief survey
Pages 1-39

Chapter II Strong approximation in finite dimensional spaces
Pages 41-75

Chapter III Strong approximation in infinite-dimensional spaces
Pages 77-167

Chapter IV Approximation problems in probability
Pages 169-200

Appendix 1 Topological vector spaces
Pages 201-213

Appendix 2 Differential Calculus in Banach spaces
Pages 215-221

Appendix 3 Differentiable Banach manifolds
Pages 223-228

Appendix 4 Probability theory
Pages 229-235

Bibliography
Pages 237-241

Index
Pages 243-245