Approximation problems in analysis and probability
This is an exposition of some special results on analytic or C & infin;-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 so...
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| Format: | eBook |
| Language: | English |
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Amsterdam
North-Holland
1989, 1989
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| Series: | North-Holland mathematics studies
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| Collection: | Elsevier eBook collection Mathematics - Collection details see MPG.ReNa |
Table of Contents:
- 11. Strong approximation
- other directionsChapter IV. Approximation problems in probability; 1. Bernstein's proof of Weierstrass theorem; 2. Some recent Bernstein-type approximation results; 3. A theorem of H. Steinhaus; 4. The Wiener process or Brownian motion; 5. Jump processes
- a theorem of Skorokhod; Appendix 1: Topological vector spaces; Appendix 2: Differential Calculus in Banach spaces; Appendix 3: Differentiable Banach manifolds; Appendix 4: Probability theory; Bibliography; Index
- Includes bibliographical references (pages 237-241)
- 2. Ci -approximation in a finite-dimensional spaceChapter III. Strong approximation in infinite-dimensional spaces; 1. Kurzweil's theorems on analytic approximation; 2. Smoothness properties of norms in Lp-spaces; 3. Ci -partitions of unity in Hilbert space; 4. Theorem of Bonic and Frampton; 5. Smale's Theorem; 6. Theorem of Eells and McAlpin; 7. Contribution of J. Wells and K. Sundaresan; 8. Theorems of Desolneux-Moulis; 9. Ck-approximation of Ck by Ci -a theorem of Heble; 10. Connection between strong approximation and earlier ideas of Bernstein-Nachbin
- Front Cover; Approximation Problems in Analysis and Probability; Copyright Page; Contents; Introduction; Chapter I. Weierstrass-Stone theorem and generalisations
- a brief survey; 1. Weierstrass-Stone theorem; 2. Closure of a module
- the weighted approximation problem; 3. Criteria of localisability; 4. A differentiable variant of the Stone-Weierstrass theorem; 5. Further differentiable variants of the Stone-Weierstrass theorem; Chapter II. Strong approximation in finite-dimensional spaces; 1. H. Whitney's theorem on analytic approximation