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010   $a9783540488149
010   $a3540488146
024 7 $a10.1007/BFb0100744
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035   $a(PQKBTitleCode)TC0000322575
035   $a(PQKBWorkID)10283691
035   $a(PQKB)10633647
035   $a(DE-He213)978-3-540-48814-9
035   $a(MiAaPQ)EBC5585318
035   $a(Au-PeEL)EBL5585318
035   $a(OCoLC)1066191013
035   $a(MiAaPQ)EBC6859942
035   $a(Au-PeEL)EBL6859942
035   $a(PPN)155203649
035   $a(EXLCZ)991000000000437309
100   $a20121227d1999      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aDifferentiability of Six Operators on Nonsmooth Functions and p-Variation /$fby R. M. Dudley, R. Norvai?a
205   $a1st ed. 1999.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1999.
215   $a1 online resource (X, 282 p.)
225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v1703
300   $aBibliographic Level Mode of Issuance: Monograph
311 08$a9783540659754 
311 08$a3540659757 
327   $aA 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.
330   $aThe book is about differentiability of six operators on functions or pairs of functions: composition (f of g), integration (of f dg), multiplication and convolution of two functions, both varying, and the product integral and inverse operators for one function. The operators are differentiable with respect to p-variation norms with optimal remainder bounds. Thus the functions as arguments of the operators can be nonsmooth, possibly discontinuous, but four of the six operators turn out to be analytic (holomorphic) for some p-variation norms. The reader will need to know basic real analysis, including Riemann and Lebesgue integration. The book is intended for analysts, statisticians and probabilists. Analysts and statisticians have each studied the differentiability of some of the operators from different viewpoints, and this volume seeks to unify and expand their results.
410  0$aLecture Notes in Mathematics,$x1617-9692 ;$v1703
606   $aOperator theory
606   $aGlobal analysis (Mathematics)
606   $aManifolds (Mathematics)
606   $aFunctions of real variables
606   $aOperator Theory
606   $aGlobal Analysis and Analysis on Manifolds
606   $aReal Functions
615  0$aOperator theory.
615  0$aGlobal analysis (Mathematics)
615  0$aManifolds (Mathematics)
615  0$aFunctions of real variables.
615 14$aOperator Theory.
615 24$aGlobal Analysis and Analysis on Manifolds.
615 24$aReal Functions.
676   $a515.724
700   $aDudley$b R. M$g(Richard M.),$048562
702   $aNorvais?a$b Rimas$f1956-
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910146307903321
996   $aDifferentiability of six operators on nonsmooth functions and p-variation$9262450
997   $aUNINA