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221028 ||| eng |
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|a 0444880216
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|a 9786611788605
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|a 1281788600
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|a 0080872700
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|a 9781281788603
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|a 9780080872704
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|a 9780444880215
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| 050 |
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4 |
|a QA221
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| 100 |
1 |
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|a Heble, M. P.
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| 245 |
0 |
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|a Approximation problems in analysis and probability
|c M.P. Heble
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| 260 |
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|a Amsterdam
|b North-Holland
|c 1989, 1989
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| 300 |
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|a xi, 245 pages
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| 505 |
0 |
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|a 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
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|a Includes bibliographical references (pages 237-241)
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|a 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
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| 505 |
0 |
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|a 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
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| 653 |
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|a Théorie de l'approximation
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| 653 |
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|a Mathematical analysis / http://id.loc.gov/authorities/subjects/sh85082116
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| 653 |
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|a Approximation, théorie de l' / ram
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| 653 |
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|a Mathematical analysis / fast / (OCoLC)fst01012068
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| 653 |
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|a Probabilities / http://id.loc.gov/authorities/subjects/sh85107090
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| 653 |
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|a Probabilités / ram
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| 653 |
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|a Analyse mathématique
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| 653 |
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|a Probabilités
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| 653 |
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|a Approximation theory / fast / (OCoLC)fst00811829
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| 653 |
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|a Probability
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| 653 |
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|a Analyse mathématique / ram
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| 653 |
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|a Approximation theory / http://id.loc.gov/authorities/subjects/sh85006190
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| 653 |
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|a MATHEMATICS / General / bisacsh
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| 653 |
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|a probability / aat
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| 653 |
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|a Probabilities / fast / (OCoLC)fst01077737
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b ZDB-1-ELC
|a Elsevier eBook collection Mathematics
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| 490 |
0 |
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|a North-Holland mathematics studies
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| 776 |
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|z 0080872700
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| 776 |
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|z 9780080872704
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| 856 |
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|u https://www.sciencedirect.com/science/bookseries/03040208/159
|x Verlag
|3 Volltext
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| 082 |
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|a 511/.4
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| 520 |
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|a 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
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