LEADER 06936nam  2201513 a 450 
001 9910789737103321
005 20200520144314.0
010   $a1-283-37995-3
010   $a9786613379955
010   $a1-4008-4269-7
024 7 $a10.1515/9781400842698
035   $a(CKB)2670000000133884
035   $a(EBL)827806
035   $a(OCoLC)769343169
035   $a(SSID)ssj0000575876
035   $a(PQKBManifestationID)11396459
035   $a(PQKBTitleCode)TC0000575876
035   $a(PQKBWorkID)10553953
035   $a(PQKB)11008932
035   $a(StDuBDS)EDZ0001756336
035   $a(DE-B1597)447361
035   $a(OCoLC)979582934
035   $a(DE-B1597)9781400842698
035   $a(Au-PeEL)EBL827806
035   $a(CaPaEBR)ebr10521870
035   $a(CaONFJC)MIL337995
035   $z(PPN)199244979
035   $a(MiAaPQ)EBC827806
035   $a(PPN)187959625
035   $a(EXLCZ)992670000000133884
100   $a20111017d2012      uy             0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aFre?chet differentiability of Lipschitz functions and porous sets in Banach spaces$b[electronic resource] /$fJoram Lindenstrauss, David Preiss, Jaroslav Tiser
205   $aCourse Book
210   $aPrinceton $cPrinceton University Press$d2012
215   $a1 online resource (436 p.)
225 1 $aAnnals of mathematics studies ;$vno. 179
300   $aDescription based upon print version of record.
311   $a0-691-15355-8 
311   $a0-691-15356-6 
320   $aIncludes bibliographical references and indexes.
327   $t Frontmatter -- $tContents -- $tChapter One: Introduction -- $tChapter Two: Gâteaux differentiability of Lipschitz functions -- $tChapter Three: Smoothness, convexity, porosity, and separable determination -- $tChapter Four: ?-Fréchet differentiability -- $tChapter Five: ?-null and ?n-null sets -- $tChapter Six: Férchet differentiability except for ?-null sets -- $tChapter Seven: Variational principles -- $tChapter Eight: Smoothness and asymptotic smoothness -- $tChapter Nine: Preliminaries to main results -- $tChapter Ten: Porosity, ?n- and ?-null sets -- $tChapter Eleven: Porosity and ?-Fréchet differentiability -- $tChapter Twelve: Fréchet differentiability of real-valued functions -- $tChapter Thirteen: Fréchet differentiability of vector-valued functions -- $tChapter Fourteen: Unavoidable porous sets and nondifferentiable maps -- $tChapter Fifteen: Asymptotic Fréchet differentiability -- $tChapter Sixteen: Differentiability of Lipschitz maps on Hilbert spaces -- $tBibliography -- $tIndex -- $tIndex of Notation
330   $aThis book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces. The book opens several new research directions in this area of geometric nonlinear functional analysis. The new methods developed here include a game approach to perturbational variational principles that is of independent interest. Detailed explanation of the underlying ideas and motivation behind the proofs of the new results on Fréchet differentiability of vector-valued functions should make these arguments accessible to a wider audience. The most important special case of the differentiability results, that Lipschitz mappings from a Hilbert space into the plane have points of Fréchet differentiability, is given its own chapter with a proof that is independent of much of the work done to prove more general results. The book raises several open questions concerning its two main topics.
410  0$aAnnals of mathematics studies ;$vno. 179.
606   $aBanach spaces
606   $aCalculus of variations
606   $aFunctional analysis
610   $aAsplund space.
610   $aBanach space.
610   $aBorel sets.
610   $aEuclidean space.
610   $aFrechet differentiability.
610   $aFréchet derivative.
610   $aFréchet differentiability.
610   $aFréchet smooth norm.
610   $aGâteaux derivative.
610   $aGâteaux differentiability.
610   $aHilbert space.
610   $aLipschitz function.
610   $aLipschitz map.
610   $aRadon-Nikodým property.
610   $aasymptotic uniform smoothness.
610   $aasymptotically smooth norm.
610   $aasymptotically smooth space.
610   $abump.
610   $acompleteness.
610   $acone-monotone function.
610   $aconvex function.
610   $adeformation.
610   $aderivative.
610   $adescriptive set theory.
610   $aflat surface.
610   $ahigher dimensional space.
610   $ainfinite dimensional space.
610   $airregular behavior.
610   $airregularity point.
610   $alinear operators.
610   $alow Borel classes.
610   $alower semicontinuity.
610   $amean value estimate.
610   $amodulus.
610   $amultidimensional mean value.
610   $anonlinear functional analysis.
610   $anonseparable space.
610   $anull sets.
610   $aperturbation function.
610   $aperturbation game.
610   $aperturbation.
610   $aporosity.
610   $aporous sets.
610   $aregular behavior.
610   $aregular differentiability.
610   $aregularity parameter.
610   $arenorming.
610   $aseparable determination.
610   $aseparable dual.
610   $aseparable space.
610   $aslice.
610   $asmooth bump.
610   $asubspace.
610   $atensor products.
610   $athree-dimensional space.
610   $atwo-dimensional space.
610   $atwo-player game.
610   $avariational principle.
610   $avariational principles.
610   $a?-null sets.
610   $a?-Fréchet derivative.
610   $a?-Fréchet differentiability.
610   $a?-porous sets.
615  0$aBanach spaces.
615  0$aCalculus of variations.
615  0$aFunctional analysis.
676   $a515/.88
686   $aSI 830$2rvk
700   $aLindenstrauss$b Joram$f1936-$041187
701   $aPreiss$b David$0515729
701   $aTis?er$b Jaroslav$f1957-$0515783
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910789737103321
996   $aFréchet differentiability of Lipschitz functions and porous sets in Banach spaces$9854568
997   $aUNINA