LEADER 04208nam 22007095 450 001 996466594303316 005 20200706074705.0 010 $a3-540-36211-8 024 7 $a10.1007/b80165 035 $a(CKB)1000000000229438 035 $a(SSID)ssj0000322521 035 $a(PQKBManifestationID)12064840 035 $a(PQKBTitleCode)TC0000322521 035 $a(PQKBWorkID)10287588 035 $a(PQKB)10790442 035 $a(DE-He213)978-3-540-36211-1 035 $a(MiAaPQ)EBC6298757 035 $a(MiAaPQ)EBC5584813 035 $a(Au-PeEL)EBL5584813 035 $a(OCoLC)51179424 035 $a(PPN)155194089 035 $a(EXLCZ)991000000000229438 100 $a20121227d2003 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aDerived Functors in Functional Analysis$b[electronic resource] /$fby Jochen Wengenroth 205 $a1st ed. 2003. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2003. 215 $a1 online resource (X, 138 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1810 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-00236-7 320 $aIncludes bibliographical references (pages [129]-132) and index. 327 $aIntroduction -- Notions from homological algebra: Derived Functors; The category of locally convex spaces -- The projective limit functor for countable spectra: Projective limits of linear spaces; The Mittag-Leffler procedure; Projective limits of locally convex spaces; Some Applications: The Mittag-Leffler theorem; Separating singularities; Surjectivity of the Cauchy-Riemann operator; Surjectivity of P(D) on spaces of smooth functions; Surjectivity of P(D) the space of distributions; Differential operators for ultradifferentiable functions of Roumieu type -- Uncountable projective spectra: Projective spectra of linear spaces; Insertion: The completion functor; Projective spectra of locally convex spaces -- The derived functors of Hom: Extk in the category of locally convex spaces; Splitting theory for Fréchet spaces; Splitting in the category of (PLS)-spaces -- Inductive spectra of locally convex spaces -- The duality functor -- References -- Index. 330 $aThe text contains for the first time in book form the state of the art of homological methods in functional analysis like characterizations of the vanishing of the derived projective limit functor or the functors Ext1 (E, F) for Fréchet and more general spaces. The researcher in real and complex analysis finds powerful tools to solve surjectivity problems e.g. on spaces of distributions or to characterize the existence of solution operators. The requirements from homological algebra are minimized: all one needs is summarized on a few pages. The answers to several questions of V.P. Palamodov who invented homological methods in analysis also show the limits of the program. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1810 606 $aFunctional analysis 606 $aCategory theory (Mathematics) 606 $aHomological algebra 606 $aPartial differential equations 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aFunctional analysis. 615 0$aCategory theory (Mathematics). 615 0$aHomological algebra. 615 0$aPartial differential equations. 615 14$aFunctional Analysis. 615 24$aCategory Theory, Homological Algebra. 615 24$aPartial Differential Equations. 676 $a515.7 700 $aWengenroth$b Jochen$4aut$4http://id.loc.gov/vocabulary/relators/aut$0451446 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466594303316 996 $aDerived functors in functional analysis$9145752 997 $aUNISA