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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...

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Detalles Bibliográficos
Autores principales: Dudley, Richard M, Norvaiša, Rimas
Lenguaje:eng
Publicado: Springer 1999
Materias:
Acceso en línea:https://dx.doi.org/10.1007/BFb0100744
http://cds.cern.ch/record/1691607
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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.
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institution Organización Europea para la Investigación Nuclear
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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