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The Resource The Localization Problem in Index Theory of Elliptic Operators, by Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin, (electronic resource)

The Localization Problem in Index Theory of Elliptic Operators, by Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin, (electronic resource)

Creator
Author
Contributor
Summary
This 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
Language
eng
Work
Publication
Extent
VIII, 117 pages 38 illustrations, 1 illustrations in color.
Contents
  • Preface
  • 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
Isbn
9783034805100
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0510-0
Instance
Label
The Localization Problem in Index Theory of Elliptic Operators
Title
The Localization Problem in Index Theory of Elliptic Operators
Statement of responsibility
by Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin
Creator
Contributor
Author
Subject
Language
eng
Summary
This 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
Member of
Cataloging source
IT-FiEUI
http://library.link/vocab/creatorName
Nazaikinskii, Vladimir
Image bit depth
0
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Schulze, Bert-Wolfgang.
  • Sternin, Boris.
  • SpringerLink (Online service)
Series statement
  • Pseudo-Differential Operators, Theory and Applications
  • Springer eBooks
Series volume
10
http://library.link/vocab/subjectName
  • Mathematics
  • K-theory
  • Functional analysis
  • Global analysis (Mathematics)
  • Differential equations, Partial
Label
The Localization Problem in Index Theory of Elliptic Operators, by Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0510-0
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Preface -- 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
Control code
978-3-0348-0510-0
Dimensions
unknown
Extent
VIII, 117 pages 38 illustrations, 1 illustrations in color.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783034805100
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-0348-0510-0
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1086520846
Label
The Localization Problem in Index Theory of Elliptic Operators, by Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0510-0
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Preface -- 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
Control code
978-3-0348-0510-0
Dimensions
unknown
Extent
VIII, 117 pages 38 illustrations, 1 illustrations in color.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783034805100
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-0348-0510-0
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1086520846

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