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Riccati map on L02(T) and its applications


Kappeler, T; Topalov, P (2005). Riccati map on L02(T) and its applications. Journal of Mathematical Analysis and Applications, 309(2):544-566.

Abstract

This 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 (T). We obtain asymptotic formulas and a priori estimates for the periodic and Dirichlet eigenvalues which generalize known results for the case of potentials q ∈ L2 (T). The key idea is to reduce the problem to a known one-the spectrum of the impedance operator-via a nonlinear analytic isomorphism between L02(T) and the Sobolev space H0-1(T). © 2004 Elsevier Inc. All rights reserved.

Abstract

This 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 (T). We obtain asymptotic formulas and a priori estimates for the periodic and Dirichlet eigenvalues which generalize known results for the case of potentials q ∈ L2 (T). The key idea is to reduce the problem to a known one-the spectrum of the impedance operator-via a nonlinear analytic isomorphism between L02(T) and the Sobolev space H0-1(T). © 2004 Elsevier Inc. All rights reserved.

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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
Uncontrolled Keywords:Hill operator; Riccati transform
Language:English
Date:2005
Deposited On:18 Feb 2010 14:27
Last Modified:06 Dec 2017 20:46
Publisher:Elsevier
ISSN:0022-247X
Publisher DOI:https://doi.org/10.1016/j.jmaa.2004.09.061

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