000 | 03230nam a22005175i 4500 | ||
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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. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1703 |
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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 |