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Differentiability of Six Operators on Nonsmooth Functions and p-Variation - Couverture souple

Dudley, Richard M.; Norvaisa, Rimas; Qian, Jinghua

 
9783540659754: Differentiability of Six Operators on Nonsmooth Functions and p-Variation
Couverture souple
ISBN 10 : 3540659757 ISBN 13 : 9783540659754
Editeur : Springer, 2008

Synopsis

The book is about differentiability of six operators on functions or pairs of functions: composition (f of g), integration (of f dg), multiplication and convolution of two functions, both varying, and the product integral and inverse operators for one function. The operators are differentiable with respect to p-variation norms with optimal remainder bounds. Thus the functions as arguments of the operators can be nonsmooth, possibly discontinuous, but four of the six operators turn out to be analytic (holomorphic) for some p-variation norms. The reader will need to know basic real analysis, including Riemann and Lebesgue integration. The book is intended for analysts, statisticians and probabilists. Analysts and statisticians have each studied the differentiability of some of the operators from different viewpoints, and this volume seeks to unify and expand their results.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l'auteur

Richard M. Dudley is a professor of mathematics at MIT. He has published over a hundred papers in peer-reviewed journals and two books. He was one of three lecturers in the 1982 St.-Flour Summer School in Probability, published in Springer's Lecture Notes in Mathematics series in 1984. Rimas Norvai?a is a principal researcher at the Institute of Mathematics and Informatics in Lithuania. Dudley and Norvai?a have written one previous book together in 1999 for Springer's Lecture Notes in Mathematics series, entitled "Differentiability of Six Operators on Nonsmooth Functions and P-Variation".

À propos de la quatrième de couverture

The book is about differentiability of six operators on functions or pairs of functions: composition (f of g), integration (of f dg), multiplication and convolution of two functions, both varying, and the product integral and inverse operators for one function. The operators are differentiable with respect to p-variation norms with optimal remainder bounds. Thus the functions as arguments of the operators can be nonsmooth, possibly discontinuous, but four of the six operators turn out to be analytic (holomorphic) for some p-variation norms. The reader will need to know basic real analysis, including Riemann and Lebesgue integration. The book is intended for analysts, statisticians and probabilists. Analysts and statisticians have each studied the differentiability of some of the operators from different viewpoints, and this volume seeks to unify and expand their results.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Springer
Date d'édition
2008
Langue
anglais
ISBN 10 
3540659757
ISBN 13 
9783540659754
Reliure
Broché
Nombre de pages
277
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