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The Resource Brownian motion and index formulas for the de Rham complex, Kazuaki Taira

Brownian motion and index formulas for the de Rham complex, Kazuaki Taira

Label
Brownian motion and index formulas for the de Rham complex
Title
Brownian motion and index formulas for the de Rham complex
Statement of responsibility
Kazuaki Taira
Creator
Subject
Language
eng
Summary
  • "The purpose of this monograph is to give an analytic proof of an index formula for the relative de Rham cohomology groups which may be considered as a generalization of the celebrated Hodge-Kodaira theory for the absolute de Rham cohomology groups."--Jacket
  • "The purpose of this monograph is to give an analytic proof of an index formula for the relative de Rham cohomology groups which may be considered as a generalization of the celebrated Hodge-Kodaira theory for the absolute de Rham cohomology groups."--BOOK JACKET
Member of
Cataloging source
OHX
http://library.link/vocab/creatorName
Taira, Kazuaki
Dewey number
530.4/75
Illustrations
illustrations
Index
index present
LC call number
QA274.75
LC item number
.T35 1998
Literary form
non fiction
Nature of contents
bibliography
Series statement
Mathematical research
Series volume
v. 106
http://library.link/vocab/subjectName
  • Brownian motion processes
  • Riemannian manifolds
  • Hodge theory
  • Complexes
  • Probabilities
  • Mouvement brownien, Processus de
  • Riemann, Variétés de
  • Hodge, Théorie de
  • Mouvement brownien, Processus de
  • Riemann, Variétés de
  • Hodge, Théorie de
  • DeRham-Komplex
  • Indexformel
  • Brownsche Bewegung
  • Euler-Poincaré-Charakteristik
  • Differentialgeometrie
  • Markov-Prozess
  • Laplace-Beltrami-Operator
  • Hodge-Zerlegung
  • Pseudodifferentialoperator
  • Elliptisches Randwertproblem
Label
Brownian motion and index formulas for the de Rham complex, Kazuaki Taira
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages [207]-209) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 35
  • 115
  • 4.7
  • Spaces of Currents
  • 118
  • Chapter 5
  • Index Formulas for the de Rham Complex
  • 121
  • 5.1
  • The Boundaryless Cases
  • 121
  • 1.3
  • 5.2
  • The Bounded Case
  • 127
  • Chapter 6
  • The Hodge-Kodaira Decomposition Theorem
  • 141
  • Chapter 7
  • The Exterior Derivative and the Codifferential Operator
  • 147
  • 7.1
  • Cotangent Bundles
  • Elementary Formulas
  • 147
  • 7.2
  • The Operators d and d*
  • 152
  • 7.3
  • The Relative Hodge-Kodaira Decomposition Theorem
  • 166
  • 7.4
  • The Hodge-Kodaira Decomposition Theorem with Boundary Condition
  • 39
  • 173
  • Chapter 8
  • The Operator D
  • 179
  • Chapter 9
  • The Long Exact Sequence and the Operator D
  • 187
  • Chapter 10
  • Proof of Theorem 9.3
  • 195
  • 1.4
  • Tensors
  • 40
  • 1.5
  • Tensors Fields
  • 42
  • Chapter 1
  • 1.6
  • Exterior Product
  • 43
  • 1.7
  • Differential Forms
  • 46
  • 1.8
  • The de Rham Complex
  • 48
  • 1.9
  • Elements of Differential Geometry
  • The Codifferential, Hodge Star and Laplace-Beltrami Operators
  • 49
  • Chapter 2
  • Elements of Functional Analysis
  • 55
  • 2.1
  • Transpose Operators
  • 55
  • 2.2
  • The Riesz Representation Theorem
  • 33
  • 56
  • 2.3
  • Closed Operators
  • 58
  • 2.4
  • Compact Operators
  • 59
  • 2.5
  • The Riesz-Schauder Theory
  • 59
  • 1.1
  • 2.6
  • Fredholm Operators
  • 61
  • 2.7
  • Adjoint Operators
  • 62
  • 2.8
  • The Hilbert-Schmidt Theory
  • 64
  • 2.9
  • Tangent Bundles
  • Theory of Semigroups
  • 65
  • Chapter 3
  • Elements of Markov Processes
  • 69
  • 3.1
  • Conditional Probabilities
  • 69
  • 3.2
  • Brownian Motion
  • 33
  • 70
  • 3.3
  • Markov Processes
  • 71
  • 3.4
  • Markov Transition Functions and Feller Semigroups
  • 73
  • 3.5
  • Theory of Feller Semigroups
  • 78
  • 1.2
  • Chapter 4
  • Elements of Partial Differential Equations
  • 85
  • 4.1
  • Sobolev Spaces
  • 85
  • 4.2
  • Fourier Integral Operators
  • 90
  • 4.3
  • Vector Fields
  • Pseudo-Differential Operators
  • 96
  • 4.4
  • Pseudo-Differential Operators on a Manifold
  • 101
  • 4.5
  • Elliptic Pseudo-Differential Operators and their Indices
  • 103
  • 4.6
  • Potentials and Pseudo-Differential Operators
Control code
40551507
Dimensions
24 cm
Edition
1st ed.
Extent
215 pages
Isbn
9783527401390
Isbn Type
(non-acid paper)
Lccn
99208045
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
Label
Brownian motion and index formulas for the de Rham complex, Kazuaki Taira
Publication
Bibliography note
Includes bibliographical references (pages [207]-209) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 35
  • 115
  • 4.7
  • Spaces of Currents
  • 118
  • Chapter 5
  • Index Formulas for the de Rham Complex
  • 121
  • 5.1
  • The Boundaryless Cases
  • 121
  • 1.3
  • 5.2
  • The Bounded Case
  • 127
  • Chapter 6
  • The Hodge-Kodaira Decomposition Theorem
  • 141
  • Chapter 7
  • The Exterior Derivative and the Codifferential Operator
  • 147
  • 7.1
  • Cotangent Bundles
  • Elementary Formulas
  • 147
  • 7.2
  • The Operators d and d*
  • 152
  • 7.3
  • The Relative Hodge-Kodaira Decomposition Theorem
  • 166
  • 7.4
  • The Hodge-Kodaira Decomposition Theorem with Boundary Condition
  • 39
  • 173
  • Chapter 8
  • The Operator D
  • 179
  • Chapter 9
  • The Long Exact Sequence and the Operator D
  • 187
  • Chapter 10
  • Proof of Theorem 9.3
  • 195
  • 1.4
  • Tensors
  • 40
  • 1.5
  • Tensors Fields
  • 42
  • Chapter 1
  • 1.6
  • Exterior Product
  • 43
  • 1.7
  • Differential Forms
  • 46
  • 1.8
  • The de Rham Complex
  • 48
  • 1.9
  • Elements of Differential Geometry
  • The Codifferential, Hodge Star and Laplace-Beltrami Operators
  • 49
  • Chapter 2
  • Elements of Functional Analysis
  • 55
  • 2.1
  • Transpose Operators
  • 55
  • 2.2
  • The Riesz Representation Theorem
  • 33
  • 56
  • 2.3
  • Closed Operators
  • 58
  • 2.4
  • Compact Operators
  • 59
  • 2.5
  • The Riesz-Schauder Theory
  • 59
  • 1.1
  • 2.6
  • Fredholm Operators
  • 61
  • 2.7
  • Adjoint Operators
  • 62
  • 2.8
  • The Hilbert-Schmidt Theory
  • 64
  • 2.9
  • Tangent Bundles
  • Theory of Semigroups
  • 65
  • Chapter 3
  • Elements of Markov Processes
  • 69
  • 3.1
  • Conditional Probabilities
  • 69
  • 3.2
  • Brownian Motion
  • 33
  • 70
  • 3.3
  • Markov Processes
  • 71
  • 3.4
  • Markov Transition Functions and Feller Semigroups
  • 73
  • 3.5
  • Theory of Feller Semigroups
  • 78
  • 1.2
  • Chapter 4
  • Elements of Partial Differential Equations
  • 85
  • 4.1
  • Sobolev Spaces
  • 85
  • 4.2
  • Fourier Integral Operators
  • 90
  • 4.3
  • Vector Fields
  • Pseudo-Differential Operators
  • 96
  • 4.4
  • Pseudo-Differential Operators on a Manifold
  • 101
  • 4.5
  • Elliptic Pseudo-Differential Operators and their Indices
  • 103
  • 4.6
  • Potentials and Pseudo-Differential Operators
Control code
40551507
Dimensions
24 cm
Edition
1st ed.
Extent
215 pages
Isbn
9783527401390
Isbn Type
(non-acid paper)
Lccn
99208045
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations

Library Locations

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      38.944377 -92.326537
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