000			03301cam a22003138i 4500
008			240510s2024 riu b 001 0 eng
020			_a9781470476663 (HB)
041			_aeng
080			_a517.98-7 _bGES
100	1		_aGesztesy, Fritz
245	1	0	_aSturm-Liouville operators, their spectral theory, and some applications
260			_aAmerican Mathematical Society _bRhode Island _c2024
300			_axv, 928p.
490	0		_aColloquium publications, _v67
500			_a Includes index.
504			_aIncludes bibliography (p. 861-905)
505			_aPreface 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
520			_ahis 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.
650		0	_aSturm-Liouville equation.
650		0	_aOperator theory.
650		0	_aSpectral theory (Mathematics)
650		7	_aOrdinary differential equations -- Boundary value problems -- Sturm-Liouville theory.
650		7	_aOrdinary differential equations -- Ordinary differential operators -- Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions.
650		7	_aOperator theory -- Special classes of linear operators -- Symmetric and selfadjoint operators (unbounded).
690			_aMathematics
700	1		_aNichols, Roger
700	1		_aZinchenko, Maxim,
942			_cBK
999			_c60704 _d60704