Ordinary differential operators
- Responsibility
- Aiping Wang, Anton Zettl
- Publication
- Providence, Rhode Island : American Mathematical Society, [2019]
- Copyright notice
- ©2019
- Physical description
- xv, 250 pages ; 27 cm
- Series
- Mathematical surveys and monographs v. 245.
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Science Library (Li and Ma)
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| Call number | Status |
|---|---|
| QA3 .A4 V.245 |
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Description
Creators/Contributors
- Author/Creator
- Wang, Aiping, 1977- author.
- Contributor
- Zettl, Anton, author.
Contents/Summary
- Bibliography
- Includes bibliographical references (pages 219-247) and index
- Contents
-
- Differential equations and expressions: First order systems Quasi-differential expressions and equations The Lagrange identity and maximal and minimal operators Deficiency indices Symmetric, self-adjoint, and dissipative operators: Regular symmetric operators Singular symmetric operators Self-adjoint operators Self-adjoint and symmetric boundary conditions Solutions and spectrum Coefficients, the deficiency index, spectrum Dissipative operators Two-interval problems: Two-interval symmetric domains Two-interval symmetric domain characterization with maximal domain functions Other topics: Green's function and adjoint problems Notation Topics not covered and open problems Bibliography Index.
- (source: Nielsen Book Data)
- Summary
-
In 1910 Herman Weyl published one of the most widely quoted papers of the 20th century in Analysis, which initiated the study of singular Sturm-Liouville problems. The work on the foundations of Quantum Mechanics in the 1920s and 1930s, including the proof of the spectral theorem for unbounded self-adjoint operators in Hilbert space by von Neumann and Stone, provided some of the motivation for the study of differential operators in Hilbert space with particular emphasis on self-adjoint operators and their spectrum. Since then the topic developed in several directions and many results and applications have been obtained. In this monograph the authors summarize some of these directions discussing self-adjoint, symmetric, and dissipative operators in Hilbert and Symplectic Geometry spaces. Part I of the book covers the theory of differential and quasi-differential expressions and equations, existence and uniqueness of solutions, continuous and differentiable dependence on initial data, adjoint expressions, the Lagrange Identity, minimal and maximal operators, etc. In Part II characterizations of the symmetric, self-adjoint, and dissipative boundary conditions are established. In particular, the authors prove the long standing Deficiency Index Conjecture. In Part III the symmetric and self-adjoint characterizations are extended to two-interval problems. These problems have solutions which have jump discontinuities in the interior of the underlying interval. These jumps may be infinite at singular interior points. Part IV is devoted to the construction of the regular Green's function. The construction presented differs from the usual one as found, for example, in the classical book by Coddington and Levinson.
(source: Nielsen Book Data)
Subjects
- Subject
- Differential operators.
- Differential operators.
- Operator theory -- Ordinary differential operators [See also 34Bxx, 34Lxx] -- Ordinary differential operators [See also 34Bxx, 34Lxx] (should also be assigned at least one other classification number.
- Ordinary differential equations -- Boundary value problems {For ordinary differential operators, see 34Lxx} -- Linear boundary value problems.
- Operator theory -- Special classes of linear operators -- Symmetric and selfadjoint operators (unbounded)
- Ordinary differential equations -- Boundary value problems {For ordinary differential operators, see 34Lxx} -- Sturm-Liouville theory [See also 34Lxx].
Bibliographic information
- Publication date
- 2019
- Copyright date
- 2019
- Series
- Mathematical surveys and monographs, 0076-5376 ; volume 245
- ISBN
- 9781470453664 (hardcover)
- 1470453665 (hardcover)
- 9781470454302 (ebook)
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