skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A class of Sturm-Liouville operators and approximate calculation of the first eigenvalues

Abstract

A special class S of Sturm-Liouville operators with simple asymptotic properties of eigenfunctions is investigated. The analytic properties of the potentials are analyzed and the operators in this class are described in terms of the transition function of the inverse problem. The following result is established: the class S is dense in the set of Sturm-Liouville operators with potentials in L{sub 2}. A subset of S that also has the density property is effectively distinguished. Based on the properties of the operators in this subset, a method of the approximate evaluation of the first eigenvalues of a Sturm-Liouville operator through its regularized traces is proposed and substantiated.

Authors:
;  [1]
  1. M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
21202755
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 189; Journal Issue: 1; Other Information: DOI: 10.1070/SM1998v189n01ABEH000298; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; DENSITY; EIGENFUNCTIONS; EIGENVALUES; EVALUATION; POTENTIALS; STURM-LIOUVILLE EQUATION

Citation Formats

Sadovnichii, V A, and Podol'skii, V E. A class of Sturm-Liouville operators and approximate calculation of the first eigenvalues. United States: N. p., 1998. Web. doi:10.1070/SM1998V189N01ABEH000298; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Sadovnichii, V A, & Podol'skii, V E. A class of Sturm-Liouville operators and approximate calculation of the first eigenvalues. United States. https://doi.org/10.1070/SM1998V189N01ABEH000298; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)
Sadovnichii, V A, and Podol'skii, V E. 1998. "A class of Sturm-Liouville operators and approximate calculation of the first eigenvalues". United States. https://doi.org/10.1070/SM1998V189N01ABEH000298; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
@article{osti_21202755,
title = {A class of Sturm-Liouville operators and approximate calculation of the first eigenvalues},
author = {Sadovnichii, V A and Podol'skii, V E},
abstractNote = {A special class S of Sturm-Liouville operators with simple asymptotic properties of eigenfunctions is investigated. The analytic properties of the potentials are analyzed and the operators in this class are described in terms of the transition function of the inverse problem. The following result is established: the class S is dense in the set of Sturm-Liouville operators with potentials in L{sub 2}. A subset of S that also has the density property is effectively distinguished. Based on the properties of the operators in this subset, a method of the approximate evaluation of the first eigenvalues of a Sturm-Liouville operator through its regularized traces is proposed and substantiated.},
doi = {10.1070/SM1998V189N01ABEH000298; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},
url = {https://www.osti.gov/biblio/21202755}, journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 1,
volume = 189,
place = {United States},
year = {Sat Feb 28 00:00:00 EST 1998},
month = {Sat Feb 28 00:00:00 EST 1998}
}