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

Journal Article · Sat Feb 28 00:00:00 EST 1998 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM1998V189N01ABEH000298; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21202755

Sadovnichii, V A; Podol'skii, V E ^[1]

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1. M.V. Lomonosov Moscow State University, Moscow (Russian Federation)

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.

• OSTI ID: 21202755
• Journal Information: Sbornik. Mathematics, Vol. 189, Issue 1; Other Information: DOI: 10.1070/SM1998v189n01ABEH000298; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
DENSITY
EIGENFUNCTIONS
EIGENVALUES
EVALUATION
POTENTIALS
STURM-LIOUVILLE EQUATION