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
3540659757, 9783540659754
DOI
10.1007/BFb0100744
ISSN
0075-8434
LCC
QA3 .L28 no. 1703,QA329.4 .L28 no. 1703
Open Library ID
OL37076M
Language
english
Format
DJVU
Filesize
2 MB (2085291 bytes)
Series
Lecture Notes in Mathematics 1703
Edition
1
Pages
282\280
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11
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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