ENGLISH

Differentiability of Six Operators on Nonsmooth Functions and p-Variation

By Richard M. Dudley , Rimas Norvaiša (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1999
ISBN
978-3-540-65975-4, 978-3-540-48814-9
DOI
10.1007/BFb0100744
Language
english
Format
PDF
Filesize
4 MB (4376390 bytes)
Series
Lecture Notes in Mathematics 1703
Edition
1
Pages
282\279
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Operator Theory; Global Analysis and Analysis on M

Description

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.

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