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Sturm-Liouville Operators, Their Spectral Theory, and Some Applications / Fritz Gesztesy, Roger Nichols, and Maxim Zinchenko.
- Format:
- Book
- Author/Creator:
- Gesztesy, Fritz, 1953- author.
- Nichols, Roger (Roger Allen), 1984- author.
- Zinchenko, Maxim, 1980- author.
- Series:
- Colloquium publications (American Mathematical Society) ; Volume 67.
- Colloquium Publications ; Volume 67
- Language:
- English
- Subjects (All):
- Sturm-Liouville equation.
- Operator theory.
- Spectral theory (Mathematics).
- Physical Description:
- 1 online resource (946 pages)
- Edition:
- First edition.
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, [2024]
- Summary:
- This book provides a detailed treatment of the various facets of modern Sturm-Liouville theory, including such topics as Weyl-Titchmarsh theory, classical, renormalized, and perturbative oscillation theory, boundary data maps, traces and determinants for Sturm-Liouville operators, strongly singular Sturm-Liouville differential operators, generalized boundary values, and Sturm-Liouville operators with distributional coefficients. To illustrate the theory, the book develops an array of examples from Floquet theory to short-range scattering theory, higher-order KdV trace relations, elliptic and algebro-geometric finite gap potentials, reflectionless potentials and the Sodin-Yuditskii class, as well as a detailed collection of singular examples, such as the Bessel, generalized Bessel, and Jacobi operators. A set of appendices contains background on the basics of linear operators and spectral theory in Hilbert spaces, Schatten-von Neumann classes of compact operators, self-adjoint extensions of symmetric operators, including the Friedrichs and Krein-von Neumann extensions, boundary triplets for ODEs, Krein-type resolvent formulas, sesquilinear forms, Nevanlinna-Herglotz functions, and Bessel functions.
- Notes:
- Description based on publisher supplied metadata and other sources.
- Description based on print version record.
- Includes bibliographical references and index.
- ISBN:
- 1-4704-7824-2
- OCLC:
- 1455135306
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