Sturm-Liouville operators, their spectral theory, and some applications (Record no. 60704)

000 -LEADER
fixed length control field 03301cam a22003138i 4500
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 240510s2024 riu b 001 0 eng
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 9781470476663 (HB)
041 ## - LANGUAGE CODE
Language code of text/sound track or separate title eng
080 ## - UNIVERSAL DECIMAL CLASSIFICATION NUMBER
Universal Decimal Classification number 517.98-7
Item number GES
100 1# - MAIN ENTRY--AUTHOR NAME
Personal name Gesztesy, Fritz
245 10 - TITLE STATEMENT
Title Sturm-Liouville operators, their spectral theory, and some applications
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication American Mathematical Society
Name of publisher Rhode Island
Year of publication 2024
300 ## - PHYSICAL DESCRIPTION
Number of Pages xv, 928p.
490 0# - SERIES STATEMENT
Series statement Colloquium publications,
Volume number/sequential designation 67
500 ## - GENERAL NOTE
General note Includes index.
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc Includes bibliography (p. 861-905)
505 ## - FORMATTED CONTENTS NOTE
Formatted contents note Preface<br/>1. Introduction<br/>2. A Bit of Physical Motivation<br/>3. Preliminaries on ODEs<br/>4. The Regular Problem on a Compact Interval [a,b] R<br/>5. The Singular Problem on (a,b) R<br/>6. The Spectral Function for a Problem with a Regular Endpoint<br/>7. The 2 2 Spectral Matrix Function in the Presence of Two Singular Interval Endpoints for the Problem on (a,b) R<br/>8. Classical Oscillation Theory, Principal Solutions, and Nonprincipal Solutions<br/>9. Renormalized Oscillation Theory<br/>10. Perturbative Oscillation Criteria and Perturbative Hardy-Type Inequalities<br/>11. Boundary Data Maps<br/>12. Spectral Zeta Functions and Computing Traces and Determinants for Sturm-Liouville Operators<br/>13. The Singular Problem on (a,), R Revisited<br/>14. Four-Coefficient Sturm-Liouville Operators and Distributional Potential Coefficients<br/>15. Epilogue: Applications to Some Partial Differential Equations of Mathematical Physics
520 ## - SUMMARY, ETC.
Summary, etc 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.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Sturm-Liouville equation.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Operator theory.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Spectral theory (Mathematics)
650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Ordinary differential equations -- Boundary value problems -- Sturm-Liouville theory.
650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Ordinary differential equations -- Ordinary differential operators -- Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions.
650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Operator theory -- Special classes of linear operators -- Symmetric and selfadjoint operators (unbounded).
690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN)
Topical term or geographic name as entry element Mathematics
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Nichols, Roger
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Zinchenko, Maxim,
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type BOOKS
Holdings
Withdrawn status Lost status Damaged status Not for loan Current library Shelving location Full call number Accession Number Koha item type
      1 IMSc Library Technical Processing 517.98-7 GES 78335 BOOKS
The Institute of Mathematical Sciences, Chennai, India

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