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Catalogue Information
Field name	Details
Dewey Class	515.724
Title	Differentiability of Six Operators on Nonsmooth Functions and p-Variation ([EBook] /) / by Richard M. Dudley, Rimas Norvaiša.
Author	Dudley, Richard M.
Added Personal Name	Norvaisa, Rimas author.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1999.
Physical Details	X, 282 p. : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1703
ISBN	9783540488149
Summary Note	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.:
Contents note	A survey on differentiability of six operators in relation to probability and statistics -- Product integrals, young integrals and p-variation -- Differentiability of the composition and quantile operators for regulated and A. E. continuous functions -- Bibliographies on p-variation and ?-variation.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/BFb0100744
Links to Related Works	Subject References: Functions of real variables . Global Analysis and Analysis on Manifolds . Global analysis (Mathematics) . Manifolds (Mathematics) . Mathematics . Operator Theory . Real Functions . Authors: Dudley, Richard M. . Norvaisa, Rimas . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 515.724 .

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Differentiability of Six Operators on Nonsmooth Functions and p-Variation

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