Sturm-Liouville operators, their spectral theory, and some applications /
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 S...
| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island :
American Mathematical Society,
[2024].
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| Series: | Colloquium publications (American Mathematical Society) ;
v. 67. |
| Subjects: |
| 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 Bessed, generalized Bessed 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 entensions, boundary triplets for ODEs, Krein-type resolvent formulas, sequilinear forms, Nevanlinna-Herglotz functions and Bessed funsctions. |
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| Physical Description: | xv, 927 pages ; 27 cm. |
| Bibliography: | Includes bibliographical references and indexes. |
| ISBN: | 9781470476663 1470476665 |