A generalization of Gordon's theorem and applications to quasiperiodic Schrödinger operators.
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Damanik, David, Stolz, Günter (2000)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Gesztesy, Fritz, Simon, Barry (2000)
Annals of Mathematics. Second Series
Boscaggin, A., Garrione, M. (2010)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
Aslanova, N.M. (2008)
Sibirskij Matematicheskij Zhurnal
Sokolov, Maksim S. (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Alexey Fedoseev (2013)
Open Mathematics
We study the inverse problem of recovering Sturm-Liouville operators on the half-line with a Bessel-type singularity inside the interval from the given Weyl function. The corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided, also necessary and sufficient conditions for the solvability of the inverse problem are obtained.
Frédéric Bourquin (1990/1991)
Numerische Mathematik
Oktay Veliev (2013)
Open Mathematics
We obtain uniform asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators L t (q) with a potential q ∈ L 1[0,1] and t-periodic boundary conditions, t ∈ (−π, π]. Using these formulas, we find sufficient conditions on the potential q such that the number of spectral singularities in the spectrum of the Hill operator L(q) in L 2(−∞,∞) is finite. Then we prove that the operator L(q) has no spectral singularities at infinity and it is an asymptotically spectral operator...
Kratz, Werner (2009)
Advances in Difference Equations [electronic only]
Fulvio Ricci, Anita Tabacco Vignati (1994)
Journal für die reine und angewandte Mathematik
George Wilson (1993)
Journal für die reine und angewandte Mathematik
Emil Horozov (2005)
Annales de l’institut Fourier
We introduce a Lie algebra, which we call adelic -algebra. Then we construct a natural bosonic representation and show that the points of the Calogero-Moser spaces are in 1:1 correspondence with the tau-functions in this representation.
Mingarelli, Angelo B. (2004)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Dwyer, H.I., Zettl, A. (1994)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Gülen Başcanbaz Tunca, Elgiz Bairamov (1999)
Czechoslovak Mathematical Journal
In this article, we consider the operator defined by the differential expression in , where is a complex valued function. Discussing the spectrum, we prove that has a finite number of eigenvalues and spectral singularities, if the condition holds. Later we investigate the properties of the principal functions corresponding to the eigenvalues and the spectral singularities.
Chyan, Chuan Jen, Henderson, Johnny (1999)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
Dwyer, H.I., Zettl, A. (1995)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Song, Changxiu (2008)
Advances in Difference Equations [electronic only]
Benchohra, M., Henderson, J., Ntouyas, S.K. (2007)
Advances in Difference Equations [electronic only]
Matthias Lesch (2000)
Journées équations aux dérivées partielles
The purpose of this note is to present several criteria for essential self-adjointness. The method is based on ideas due to Shubin. This note is divided into two parts. The first part deals with symmetric first order systems on the line in the most general setting. Such a symmetric first order system of differential equations gives rise naturally to a symmetric linear relation in a Hilbert space. In this case even regularity is nontrivial. We will announce a regularity result and discuss criteria...
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