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| Softcover ISBN: | 978-0-8218-1589-2 |
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| Softcover ISBN: | 978-0-8218-1589-2 |
| Product Code: | MMONO/39 |
| List Price: | $165.00 |
| MAA Member Price: | $148.50 |
| AMS Member Price: | $132.00 |
| eBook ISBN: | 978-1-4704-4454-9 |
| Product Code: | MMONO/39.E |
| List Price: | $155.00 |
| MAA Member Price: | $139.50 |
| AMS Member Price: | $124.00 |
| Softcover ISBN: | 978-0-8218-1589-2 |
| eBook ISBN: | 978-1-4704-4454-9 |
| Product Code: | MMONO/39.B |
| List Price: | $320.00 $242.50 |
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Book DetailsTranslations of Mathematical MonographsVolume: 39; 1975; 525 ppMSC: Primary 34; Secondary 47
This monograph is devoted to the spectral theory of the Sturm- Liouville operator and to the spectral theory of the Dirac system. In addition, some results are given for nth order ordinary differential operators. Those parts of this book which concern nth order operators can serve as simply an introduction to this domain, which at the present time has already had time to become very broad. For the convenience of the reader who is not familar with abstract spectral theory, the authors have inserted a chapter (Chapter 13) in which they discuss this theory, concisely and in the main without proofs, and indicate various connections with the spectral theory of differential operators.
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Table of Contents
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Chapters
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Expansion in a Finite Interval
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Eigenfunction Expansions for a Sturm-Liouville Operator for the Case of an Infinite Interval
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Expansion in the Singular Case for a Dirac System
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Investigation of the Spectrum
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Examples
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Solution of the Cauchy Problem for the One-dimensional Wave Equation
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Eigenfunction Expansion of a Sturm-Liouville Operator
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Differentiation of an Eigenfunction Expansion
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Solution of the Cauchy Problem for a One-Dimensional Dirac System
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Asymptotic Behaviour of the Spectral Kernel and its Derivatives for the Case of a Dirac System
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Expansion, and Differentiation of an Expansion, with Respect to the Eigenfunctions of a Dirac System
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Asymptotic Behaviour of the Number of Eigenvalues of a Sturm-Liouville Operator
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Elements of the Spectral Theory of Linear Operators in Hilbert Space. Relation to Differential Operators
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Some Theorems of Analysis
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This monograph is devoted to the spectral theory of the Sturm- Liouville operator and to the spectral theory of the Dirac system. In addition, some results are given for nth order ordinary differential operators. Those parts of this book which concern nth order operators can serve as simply an introduction to this domain, which at the present time has already had time to become very broad. For the convenience of the reader who is not familar with abstract spectral theory, the authors have inserted a chapter (Chapter 13) in which they discuss this theory, concisely and in the main without proofs, and indicate various connections with the spectral theory of differential operators.
-
Chapters
-
Expansion in a Finite Interval
-
Eigenfunction Expansions for a Sturm-Liouville Operator for the Case of an Infinite Interval
-
Expansion in the Singular Case for a Dirac System
-
Investigation of the Spectrum
-
Examples
-
Solution of the Cauchy Problem for the One-dimensional Wave Equation
-
Eigenfunction Expansion of a Sturm-Liouville Operator
-
Differentiation of an Eigenfunction Expansion
-
Solution of the Cauchy Problem for a One-Dimensional Dirac System
-
Asymptotic Behaviour of the Spectral Kernel and its Derivatives for the Case of a Dirac System
-
Expansion, and Differentiation of an Expansion, with Respect to the Eigenfunctions of a Dirac System
-
Asymptotic Behaviour of the Number of Eigenvalues of a Sturm-Liouville Operator
-
Elements of the Spectral Theory of Linear Operators in Hilbert Space. Relation to Differential Operators
-
Some Theorems of Analysis
