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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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Heble, M. P.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Amsterdam ; New York : New York, N.Y., U.S.A. : North-Holland ; Distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1989.
Colección:North-Holland mathematics studies ; 159.
Temas:
Approximation theory.
Mathematical analysis.
Probabilities.
Probability
Th�eorie de l'approximation.
Analyse math�ematique.
Probabilit�es.
probability.
MATHEMATICS > General.
Approximation theory
Mathematical analysis
Probabilities
Approximation, th�eorie de l'.
Acceso en línea:Texto completo
Texto completo
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MARC

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100 1 |a Heble, M. P. 
245 1 0 |a Approximation problems in analysis and probability /  |c M.P. Heble. 
260 |a Amsterdam ;  |a New York :  |b North-Holland ;  |a New York, N.Y., U.S.A. :  |b Distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.,  |c 1989. 
300 |a 1 online resource (xi, 245 pages) 
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490 1 |a North-Holland mathematics studies ;  |v 159 
520 |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. 
504 |a Includes bibliographical references (pages 237-241). 
588 0 |a Print version record. 
505 0 |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 
505 8 |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 
505 8 |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 
546 |a English. 
650 0 |a Approximation theory. 
650 0 |a Mathematical analysis. 
650 0 |a Probabilities. 
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776 0 8 |i Print version:  |a Heble, M.P.  |t Approximation problems in analysis and probability.  |d 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  |z 0444880216  |z 9780444880215  |w (DLC) 89016147  |w (OCoLC)20012521 
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