000 03230nam a22005175i 4500
001 978-3-540-48814-9
003 DE-He213
005 20190213151625.0
007 cr nn 008mamaa
008 121227s1999 gw | s |||| 0|eng d
020 _a9783540488149
_9978-3-540-48814-9
024 7 _a10.1007/BFb0100744
_2doi
050 4 _aQA329-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
072 7 _aPBKF
_2thema
082 0 4 _a515.724
_223
100 1 _aDudley, Richard M.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aDifferentiability of Six Operators on Nonsmooth Functions and p-Variation
_h[electronic resource] /
_cby Richard M. Dudley, Rimas Norvaiša.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1999.
300 _aX, 282 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1703
505 0 _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.
520 _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.
650 0 _aOperator theory.
650 0 _aGlobal analysis.
650 0 _aMathematics.
650 1 4 _aOperator Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M12139
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
_0http://scigraph.springernature.com/things/product-market-codes/M12082
650 2 4 _aReal Functions.
_0http://scigraph.springernature.com/things/product-market-codes/M12171
700 1 _aNorvaiša, Rimas.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662183403
776 0 8 _iPrinted edition:
_z9783540659754
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1703
856 4 0 _uhttps://doi.org/10.1007/BFb0100744
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11314
_d11314