UID:
almahu_9947368103902882
Format:
1 online resource (433 p.)
ISBN:
1-283-52586-0
,
9786613838315
,
0-08-095424-3
Series Statement:
North-Holland mathematical library ; v. 17
Uniform Title:
Einige Klassen singulärer Gleichungen.
Content:
This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field.
Note:
Translation of Einige Klassen singularer Gleichungen.
,
Front Cover; Some Classes of Singular Equations; Copyright Page; CONTENTS; Introduction; Chapter 1. Noether Operators; 1.1 Some Fundamental Concepts and Notations; 1.2 Projections and Normally Solvable Operators; 1.3 Noether Operators; 1.4 Operators with Bounded Regularizer; 1.5 Operators with Unbounded Regularizer; 1.6 Comments and References; Chapter 2. Abstract Singular Equations of Normal Type; 2.1 An Algebra of Operator Functions; 2.2 Abstract Singular Equations; 2.3 Factorization of Functions; 2.4 Application of the Factorization to the Solution of Singular Equations
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2.5 Comments and ReferencesChapter 3. Special Singular Equations of Normal Type; 3.1 Discrete Wiener-Hopf Equations; 3.2 Wiener-Hopf Integral Equations; 3.3 Paired Wiener-Hopf Equations; 3.4 Singular Integral Equations; 3.5 Comments and References; Chapter 4. Abstract Singular Equations of Non-Normal Type; 4.1 The Method of Special Factorization; 4.2 Wiener-Hopf Equations; 4.3 Abstract Singular Equations; 4.4 An Algebra of Singular Operators; 4.5 The Method of Left Regularization; 4.6 Comments and References
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Chapter 5. Wiener-Hopf Integral Equations of Non-Normal Type and their Discrete Analogue5.1 Discrete Wiener-Hopf Equations; 5.2 Wiener-Hopf Integral Equations; 5.3 Paired Discrete Wiener-Hopf Equations; 5.4 Paired Wiener-Hopf Integral Equations; 5.5 Non-Bounded Regularization of Paired Wiener-Hopf Equations; 5.6 Comments and References; Chapter 6. Singular Integral Equations of Non -Normal Type; 6.1 Lemmas; 6.2 The Spaces Generated by Zeros of the Symbol; 6.3 Symbols with Zeros of Integral Orders; 6.4 Symbols with Zeros of Non-Integral Orders; 6.5 A More General Case of Degeneration
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6.6 The Solution of a Singular Integral Equation of Non-Normal Type by Means of Factorization6.7 Non-Bounded Regularization of Singular Integral Equations of Non-Normal Type; 6.8 Comments and References; Chapter 7. Systems of Singular Equations of Normal Type; 7.1 A Theorem on Operator Matrices; 7.2 Factorization of Matrix Functions; 7.3 Systems of Abstract Singular Equations; 7.4 Systems of Wiener-Hopf Equations; 7.5 Systems of Singular Integral Equations; 7.6 Comments and References; Chapter 8. Systems of Singular Equations of Non-Normal Type
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8.1 Representations of Singular Matrix Functions8.2 Systems of Discrete Wiener-Hopf Equations; 8.3 Systems of Wiener-Hopf Integral Equations; 8.4 Systems of Paired Wiener-Hopf Equations; 8.5 Systems of Singular Integral Equations; 8.6 Non-Bounded Regularization of Systems of Singular Integral Equations; 8.7 Comments and References; Chapter 9. Singular Equations in some Countably Normed Spaces and Spaces of Distributions; 9.1 Operator Equations in Distribution Spaces; 9.2 Discrete Wiener-Hopf Equations; 9.3 Wiener-Hopf Integral Equations; 9.4 Singular Integral Equations
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9.5 Comments and References
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English
Additional Edition:
ISBN 0-7204-0501-7
Language:
English
