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• catalog abstract ""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.".
• catalog contributor b11037993.
• catalog created "1998.".
• catalog date "1998".
• catalog date "1998.".
• catalog dateCopyrighted "1998.".
• catalog description ""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.".
• catalog description "Chapter 1 Elements of Differential Geometry 33 -- 1.1 Tangent Bundles 33 -- 1.2 Vector Fields 35 -- 1.3 Cotangent Bundles 39 -- 1.4 Tensors 40 -- 1.5 Tensors Fields 42 -- 1.6 Exterior Product 43 -- 1.7 Differential Forms 46 -- 1.8 The de Rham Complex 48 -- 1.9 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 56 -- 2.3 Closed Operators 58 -- 2.4 Compact Operators 59 -- 2.5 The Riesz-Schauder Theory 59 -- 2.6 Fredholm Operators 61 -- 2.7 Adjoint Operators 62 -- 2.8 The Hilbert-Schmidt Theory 64 -- 2.9 Theory of Semigroups 65 -- Chapter 3 Elements of Markov Processes 69 -- 3.1 Conditional Probabilities 69 -- 3.2 Brownian Motion 70 -- 3.3 Markov Processes 71 -- 3.4".
• catalog description "Includes bibliographical references (p. [207]-209) and index.".
• catalog description "Markov Transition Functions and Feller Semigroups 73 -- 3.5 Theory of Feller Semigroups 78 -- Chapter 4 Elements of Partial Differential Equations 85 -- 4.1 Sobolev Spaces 85 -- 4.2 Fourier Integral Operators 90 -- 4.3 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 115 -- 4.7 Spaces of Currents 118 -- Chapter 5 Index Formulas for the de Rham Complex 121 -- 5.1 The Boundaryless Cases 121 -- 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 Elementary Formulas 147 -- 7.2 The Operators d and d* 152 -- 7.3 The Relative Hodge-Kodaira Decomposition Theorem 166 -- 7.4".
• catalog description "The Hodge-Kodaira Decomposition Theorem with Boundary Condition 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.".
• catalog extent "215 p. :".
• catalog identifier "3527401393".
• catalog isPartOf "Mathematical research ; Bd. 106".
• catalog issued "1998".
• catalog issued "1998.".
• catalog language "eng".
• catalog publisher "Berlin : Wiley-VCH,".
• catalog subject "Brownian motion processes.".
• catalog subject "Hodge theory.".
• catalog subject "QA274.75 .T357 1998".
• catalog subject "Riemannian manifolds.".
• catalog tableOfContents "Chapter 1 Elements of Differential Geometry 33 -- 1.1 Tangent Bundles 33 -- 1.2 Vector Fields 35 -- 1.3 Cotangent Bundles 39 -- 1.4 Tensors 40 -- 1.5 Tensors Fields 42 -- 1.6 Exterior Product 43 -- 1.7 Differential Forms 46 -- 1.8 The de Rham Complex 48 -- 1.9 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 56 -- 2.3 Closed Operators 58 -- 2.4 Compact Operators 59 -- 2.5 The Riesz-Schauder Theory 59 -- 2.6 Fredholm Operators 61 -- 2.7 Adjoint Operators 62 -- 2.8 The Hilbert-Schmidt Theory 64 -- 2.9 Theory of Semigroups 65 -- Chapter 3 Elements of Markov Processes 69 -- 3.1 Conditional Probabilities 69 -- 3.2 Brownian Motion 70 -- 3.3 Markov Processes 71 -- 3.4".
• catalog tableOfContents "Markov Transition Functions and Feller Semigroups 73 -- 3.5 Theory of Feller Semigroups 78 -- Chapter 4 Elements of Partial Differential Equations 85 -- 4.1 Sobolev Spaces 85 -- 4.2 Fourier Integral Operators 90 -- 4.3 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 115 -- 4.7 Spaces of Currents 118 -- Chapter 5 Index Formulas for the de Rham Complex 121 -- 5.1 The Boundaryless Cases 121 -- 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 Elementary Formulas 147 -- 7.2 The Operators d and d* 152 -- 7.3 The Relative Hodge-Kodaira Decomposition Theorem 166 -- 7.4".
• catalog tableOfContents "The Hodge-Kodaira Decomposition Theorem with Boundary Condition 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.".
• catalog title "Brownian motion and index formulas for the de Rham complex / Kazuaki Taira.".
• catalog type "text".