000			04232nam a22005295i 4500
001			978-3-0348-0510-0
003			DE-He213
005			20140220082506.0
007			cr nn 008mamaa
008			131125s2014 sz | s |||| 0|eng d
020			_a9783034805100 _9978-3-0348-0510-0
024	7		_a10.1007/978-3-0348-0510-0 _2doi
050		4	_aQA614-614.97
072		7	_aPBKS _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a514.74 _223
100	1		_aNazaikinskii, Vladimir. _eauthor.
245	1	4	_aThe Localization Problem in Index Theory of Elliptic Operators _h[electronic resource] / _cby Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin.
264		1	_aBasel : _bSpringer Basel : _bImprint: Birkhäuser, _c2014.
300			_aVIII, 117 p. 38 illus., 1 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aPseudo-Differential Operators, Theory and Applications ; _v10
505	0		_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.
520			_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.
650		0	_aMathematics.
650		0	_aK-theory.
650		0	_aFunctional analysis.
650		0	_aGlobal analysis.
650		0	_aDifferential equations, partial.
650	1	4	_aMathematics.
650	2	4	_aGlobal Analysis and Analysis on Manifolds.
650	2	4	_aK-Theory.
650	2	4	_aFunctional Analysis.
650	2	4	_aPartial Differential Equations.
700	1		_aSchulze, Bert-Wolfgang. _eauthor.
700	1		_aSternin, Boris. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783034805094
830		0	_aPseudo-Differential Operators, Theory and Applications ; _v10
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-0348-0510-0
912			_aZDB-2-SMA
999			_c92439 _d92439