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Approximation problems in analysis and probability
Title:
Approximation problems in analysis and probability
Author:
Heble, M. P.
ISBN:
9780444880215
9780080872704
9781281788603
9786611788605
Personal Author:
Publication Information:
Amsterdam ; New York : North-Holland ; New York, N.Y., U.S.A. : Distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1989.
Physical Description:
1 online resource (xi, 245 pages).
Series:
North-Holland mathematics studies ; 159
North-Holland mathematics studies ; 159.
Contents:
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
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
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
Abstract:
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 some recent results by the author on strong C & infin;-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.
Genre:
Electronic Access:
ScienceDirect http://www.sciencedirect.com/science/book/9780444880215 ScienceDirect http://www.sciencedirect.com/science/publication?issn=03040208&volume=159Available:*
Shelf Number | Item Barcode | Shelf Location | Status |
|---|---|---|---|
| QA221 .H375 1989 EB | 1191269-1001 | Elsevier E-Book Collections | Searching... |
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