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＜E-Book＞
Differentiability of Six Operators on Nonsmooth Functions and p-Variation / by R. M. Dudley, R. Norvaiša
(Lecture Notes in Mathematics. ISSN:16179692 ; 1703)

Edition	1st ed. 1999.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	1999
Language	English
Size	X, 282 p : online resource
Authors	*Dudley, R. M author Norvaiša, R author SpringerLink (Online service)
Subjects	LCSH:Operator theory LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Functions of real variables FREE:Operator Theory FREE:Global Analysis and Analysis on Manifolds FREE:Real Functions
Notes	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 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 HTTP:URL=https://doi.org/10.1007/BFb0100744

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