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Riccati Representation for Elements in H-1(T) and its Applications


Kappeler, T; Topalov, P (2003). Riccati Representation for Elements in H-1(T) and its Applications. Pliska Bulgarski Matematicheski Studii, 15:171-188.

Abstract

The paper is concerned with the spectral properties of the Schrödinger operator Lq def= − d2/dx2 + q with periodic potential q from the Sobolev space H −1 (T1 ). We obtain asymptotic formulas and a priori estimates for the periodic and Dirichlet eigenvalues which generalize known results for the case of potentials q ∈ L 2 0 (T1 ). The key idea is to reduce the problem to a known one – the spectrum of the impedance operator – via a nonlinear analytic isomorphism of the Sobolev spaces H −1 0 (T1 ) and L2 0 (T1 ).

Abstract

The paper is concerned with the spectral properties of the Schrödinger operator Lq def= − d2/dx2 + q with periodic potential q from the Sobolev space H −1 (T1 ). We obtain asymptotic formulas and a priori estimates for the periodic and Dirichlet eigenvalues which generalize known results for the case of potentials q ∈ L 2 0 (T1 ). The key idea is to reduce the problem to a known one – the spectrum of the impedance operator – via a nonlinear analytic isomorphism of the Sobolev spaces H −1 0 (T1 ) and L2 0 (T1 ).

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2003
Deposited On:18 Feb 2010 13:18
Last Modified:05 Apr 2016 13:25
Publisher:Institute of Mathematics and Informatics. Bulgarian Academy of Sciences
ISSN:0204-9805
Official URL:http://www.math.bas.bg/~pliska
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2071691

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