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 |