Approximation Problems in Analysis and Probability - 1st Edition - ISBN: 9780444880215, 9780080872704

Approximation Problems in Analysis and Probability, Volume 159

1st Edition

Authors: M.P. Heble
eBook ISBN: 9780080872704
Imprint: North Holland
Published Date: 1st January 1989
Page Count: 244
Sales tax will be calculated at check-out Price includes VAT/GST
Price includes VAT/GST
× DRM-Free

Easy - Download and start reading immediately. There’s no activation process to access eBooks; all eBooks are fully searchable, and enabled for copying, pasting, and printing.

Flexible - Read on multiple operating systems and devices. Easily read eBooks on smart phones, computers, or any eBook readers, including Kindle.

Open - Buy once, receive and download all available eBook formats, including PDF, EPUB, and Mobi (for Kindle).

Institutional Access

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.

Table of Contents

Weierstrass-Stone Theorem and Generalisations - A Brief Survey. Weierstrass-Stone Theorem. Closure of a Module - The Weighted Approximation Problem. Criteria of Localisability. A Differentiable Variant of the Stone-Weierstrass Theorem. Further Differentiable Variants of the Stone-Weierstrass Theorem.

Strong Approximation in Finite-Dimensional Spaces. H. Whitney's Theorem on Analytic Approximation. C∞- Approximation in a Finite-Dimensional Space.

Strong Approximation in Infinite-Dimensional Spaces. Kurzweil's Theorems on Analytic Approximation. Smoothness Properties of Norms in Lp-Spaces. C∞-Partitions of Unity in Hilbert Space. Theorem of Bonic and Frampton. Smale's Theorem. Theorem of Eells and McAlpin. Contributions of J. Wells and K. Sundaresan. Theorems of Desolneux-Moulis. Ck-Approximation of Ck by C∞ - A Theorem of Heble. Connection Between Strong Approximation and Earlier Ideas of Bernstein-Nachbin. Strong Approximation - Other Directions.

Approximation Problems in Probability. Bernstein's Proof of Weierstrass' Theorem. Some Recent Bernstein-Type Approximation Results. A Theorem of H. Steinhaus. The Wiener Process or Brownian Motion. Jump Processes - A Theorem of Skorokhod. Appendices:

  1. Topological Vector Spaces.
  2. Differential Calculus in Banach Spaces.
  3. Differentiable Banach Manifolds.
  4. Probability Theory. Bibliography. Index.


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.


No. of pages:
© North Holland 1989
North Holland
eBook ISBN:


@from:R.M. Aron @qu:...its treatment of approximation in infinite-dimensional spaces provides a welcome, different approach which supplements the existing body of work in this field. @source:Mathematical Reviews @qu:The author has made important contributions... @source:Zentralblatt für Mathematik

Ratings and Reviews

About the Authors

M.P. Heble Author