TY  - BOOK
AU  - Gesztesy,Fritz
AU  - Nichols,Roger
AU  - Zinchenko,Maxim
TI  - Sturm-Liouville operators, their spectral theory, and some applications 
T2  - Colloquium publications,
SN  - 9781470476663 (HB)
PY  - 2024///
CY  - American Mathematical Society
PB  - Rhode Island
KW  - Sturm-Liouville equation
KW  - Operator theory
KW  - Spectral theory (Mathematics)
KW  - Ordinary differential equations -- Boundary value problems -- Sturm-Liouville theory
KW  - Ordinary differential equations -- Ordinary differential operators -- Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions
KW  - Operator theory -- Special classes of linear operators -- Symmetric and selfadjoint operators (unbounded)
N1  -  Includes index; Includes bibliography (p. 861-905); Preface
1. Introduction
2. A Bit of Physical Motivation
3. Preliminaries on ODEs
4. The Regular Problem on a Compact Interval [a,b] R
5. The Singular Problem on (a,b) R
6. The Spectral Function for a Problem with a Regular Endpoint
7. The 2 2 Spectral Matrix Function in the Presence of Two Singular Interval Endpoints for the Problem on (a,b) R
8. Classical Oscillation Theory, Principal Solutions, and Nonprincipal Solutions
9. Renormalized Oscillation Theory
10. Perturbative Oscillation Criteria and Perturbative Hardy-Type Inequalities
11. Boundary Data Maps
12. Spectral Zeta Functions and Computing Traces and Determinants for Sturm-Liouville Operators
13. The Singular Problem on (a,), R Revisited
14. Four-Coefficient Sturm-Liouville Operators and Distributional Potential Coefficients
15. Epilogue: Applications to Some Partial Differential Equations of Mathematical Physics
N2  - his 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 Strum-Liouville differential operators, generalized boundary values, and Strum-Liouville operators with distributional coefficients. To illustrate the teory, the book develops an array of examples from Floquet theory to short-range scattering theory, higher order KdV trace relations, elloptic 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 summetric 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
ER  -