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Spectral analysis of differential operators : interplay between spectral and oscillatory properties
Autor: Fedor S. Rofe-Beketov, Aleksandr M. Kholkin
Rok: 2005
ISBN: 9789812562760
OKCZID: 110429983
Citace (dle ČSN ISO 690):
ROFE-BEKETOV, Fedor S, KHOLʹKIN, Aleksandr M., ed. a MILATOVIC, Ognjen, ed. Spectral analysis of differential operators: interplay between spectral and oscillatory properties [elektronický zdroj]. Hackensack, NJ: World Scientific, c2005. xxiii, 438 p. World Scientific monograph series in mathematics, v. 7.
Anotace
This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigated in the book is the behavior of discrete eigenvalues which appear in spectral gaps of the Hill operator and almost periodic Schrödinger operators due to local perturbations of the potential (e.g., modeling impurities in crystals). The book is based on results that have not been presented in other monographs. The only prerequisites needed to read it are basics of ordinary differential equations and operator theory. It should be accessible to graduate students, though its main topics are of interest to research mathematicians working in functional analysis, differential equations and mathematical physics, as well as to physicists interested in spectral theory of differential operators.