LEADER 05246nam 22007335 450 001 9910300141703321 005 20220405171035.0 010 $a3-0348-0510-1 024 7 $a10.1007/978-3-0348-0510-0 035 $a(CKB)3710000000074763 035 $a(EBL)1593005 035 $a(SSID)ssj0001067640 035 $a(PQKBManifestationID)11581037 035 $a(PQKBTitleCode)TC0001067640 035 $a(PQKBWorkID)11079781 035 $a(PQKB)11761474 035 $a(MiAaPQ)EBC1593005 035 $a(DE-He213)978-3-0348-0510-0 035 $a(PPN)176102884 035 $a(EXLCZ)993710000000074763 100 $a20131125d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe localization problem in index theory of elliptic operators /$fby Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin 205 $a1st ed. 2014. 210 1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2014. 215 $a1 online resource (122 p.) 225 1 $aPseudo-Differential Operators, Theory and Applications,$x2297-0355 ;$v10 300 $aDescription based upon print version of record. 311 $a3-0348-0509-8 320 $aIncludes bibliographical references and index. 327 $aPreface -- Introduction -- 0.1 Basics of Elliptic Theory -- 0.2 Surgery and the Superposition Principle -- 0.3 Examples and Applications -- 0.4 Bibliographical Remarks -- Part I: Superposition Principle -- 1 Superposition Principle for the Relative Index -- 1.1 Collar Spaces -- 1.2 Proper Operators and Fredholm Operators -- 1.3 Superposition Principle -- 2 Superposition Principle for K-Homology -- 2.1 Preliminaries -- 2.2 Fredholm Modules and K-Homology -- 2.3 Superposition Principle -- 2.4 Fredholm Modules and Elliptic Operators -- 3 Superposition Principle for KK-Theory -- 3.1 Preliminaries -- 3.2 Hilbert Modules, Kasparov Modules, and KK -- 3.3 Superposition Principle -- Part II: Examples -- 4 Elliptic Operators on Noncompact Manifolds -- 4.1 Gromov?Lawson Theorem -- 4.2 Bunke Theorem -- 4.3 Roe?s Relative Index Construction -- 5 Applications to Boundary Value Problems -- 5.1 Preliminaries -- 5.2 Agranovich?Dynin Theorem -- 5.3 Agranovich Theorem -- 5.4 Bojarski Theorem and Its Generalizations -- 5.5 Boundary Value Problems with Symmetric Conormal Symbol -- 6 Spectral Flow for Families of Dirac Type Operators -- 6.1 Statement of the Problem -- 6.2 Simple Example -- 6.3 Formula for the Spectral Flow -- 6.4 Computation of the Spectral Flow for a Graphene Sheet -- Bibliography. 330 $aThis book deals with the localization approach to the index problem for elliptic operators. Localization ideas have been widely used for solving various specific index problems for a long time, but the fact that there is actually a fundamental localization principle underlying all these solutions has mostly passed unnoticed. The ignorance of this general principle has often necessitated using various artificial tricks and hindered the solution of important new problems in index theory. So far, the localization principle has scarcely been covered in journal papers. The present book is intended to fill this gap. Both the general localization principle and its applications to specific problems, old and new, are covered. Concisely and clearly written, this monograph includes numerous figures helping the reader to visualize the material. The Localization Problem in Index Theory of Elliptic Operators will be of interest to researchers as well as graduate and postgraduate students specializing in differential equations and related topics. 410 0$aPseudo-Differential Operators, Theory and Applications,$x2297-0355 ;$v10 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aK-theory 606 $aFunctional analysis 606 $aDifferential equations, Partial 606 $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082 606 $aK-Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11086 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aGlobal analysis (Mathematics) 615 0$aManifolds (Mathematics) 615 0$aK-theory. 615 0$aFunctional analysis. 615 0$aDifferential equations, Partial. 615 14$aGlobal Analysis and Analysis on Manifolds. 615 24$aK-Theory. 615 24$aFunctional Analysis. 615 24$aPartial Differential Equations. 676 $a515.7242 676 $a515.7242 700 $aNazaikinskii$b Vladimir$4aut$4http://id.loc.gov/vocabulary/relators/aut$0722020 702 $aSchulze$b Bert-Wolfgang$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSternin$b Boris$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910300141703321 996 $aThe Localization Problem in Index Theory of Elliptic Operators$92516597 997 $aUNINA