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Home > Mathematics and Science Textbooks > Mathematics > Calculus and mathematical analysis > Approximation Problems in Analysis and Probability: Volume 159(Volume 159 North-Holland Mathematics Studies)
Approximation Problems in Analysis and Probability: Volume 159(Volume 159 North-Holland Mathematics Studies)

Approximation Problems in Analysis and Probability: Volume 159(Volume 159 North-Holland Mathematics Studies)


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About the Book

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.

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.

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


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Product Details
  • ISBN-13: 9780444880215
  • Publisher: Elsevier Science & Technology
  • Publisher Imprint: North-Holland
  • Language: English
  • Series Title: Volume 159 North-Holland Mathematics Studies
  • ISBN-10: 0444880216
  • Publisher Date: 01 Jan 1989
  • Binding: Hardback
  • No of Pages: 244
  • Sub Title: Volume 159


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Approximation Problems in Analysis and Probability: Volume 159(Volume 159 North-Holland Mathematics Studies)
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