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Differentiability of six operators on nonsmooth functions and p-variation
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...
Autores principales: | , |
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Lenguaje: | eng |
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Springer
1999
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Acceso en línea: | https://dx.doi.org/10.1007/BFb0100744 http://cds.cern.ch/record/1691607 |
_version_ | 1780935790221590528 |
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author | Dudley, Richard M Norvaiša, Rimas |
author_facet | Dudley, Richard M Norvaiša, Rimas |
author_sort | Dudley, Richard M |
collection | CERN |
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. |
id | cern-1691607 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 1999 |
publisher | Springer |
record_format | invenio |
spelling | cern-16916072021-04-21T21:08:34Zdoi:10.1007/BFb0100744http://cds.cern.ch/record/1691607engDudley, Richard MNorvaiša, RimasDifferentiability of six operators on nonsmooth functions and p-variationMathematical Physics and MathematicsThe 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.Springeroai:cds.cern.ch:16916071999 |
spellingShingle | Mathematical Physics and Mathematics Dudley, Richard M Norvaiša, Rimas Differentiability of six operators on nonsmooth functions and p-variation |
title | Differentiability of six operators on nonsmooth functions and p-variation |
title_full | Differentiability of six operators on nonsmooth functions and p-variation |
title_fullStr | Differentiability of six operators on nonsmooth functions and p-variation |
title_full_unstemmed | Differentiability of six operators on nonsmooth functions and p-variation |
title_short | Differentiability of six operators on nonsmooth functions and p-variation |
title_sort | differentiability of six operators on nonsmooth functions and p-variation |
topic | Mathematical Physics and Mathematics |
url | https://dx.doi.org/10.1007/BFb0100744 http://cds.cern.ch/record/1691607 |
work_keys_str_mv | AT dudleyrichardm differentiabilityofsixoperatorsonnonsmoothfunctionsandpvariation AT norvaisarimas differentiabilityofsixoperatorsonnonsmoothfunctionsandpvariation |