Schrödinger operators with a singular potential.
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Diagana, Toka (2002)
International Journal of Mathematics and Mathematical Sciences
Herbert Leinfelder, C.G. Simader (1981)
Mathematische Zeitschrift
Werner Stork (1975)
Mathematische Zeitschrift
Klaus Gero Kalb (1978)
Mathematische Annalen
Maksim Sokolov (2005)
Open Mathematics
In the current work a generalization of the famous Weyl-Kodaira inversion formulas for the case of self-adjoint differential vector-operators is proved. A formula for spectral resolutions over an analytical defining set of solutions is discussed. The article is the first part of the planned two-part survey on the structural spectral theory of self-adjoint differential vector-operators in matrix Hilbert spaces.
Palle E.T. Jorgensen (1979)
Mathematische Zeitschrift
Andrea Posilicano (2003)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Let be the symmetric operator given by the restriction of to , where is a self-adjoint operator on the Hilbert space and is a linear dense set which is closed with respect to the graph norm on , the operator domain of . We show that any self-adjoint extension of such that can be additively decomposed by the sum , where both the operators and take values in the strong dual of . The operator is the closed extension of to the whole whereas is explicitly written in terms...
Jan Janas, Jan Stochel (1997)
Annales Polonici Mathematici
A generalization of the Carleman criterion for selfadjointness of Jacobi matrices to the case of symmetric matrices with finite rows is established. In particular, a new proof of the Carleman criterion is found. An extension of Jørgensen's criterion for selfadjointness of symmetric operators with "almost invariant" subspaces is obtained. Some applications to hyponormal weighted shifts are given.
Milatovic, Ognjen (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Yuriĭ Samoĭlenko, Lyudmila Turowska (1997)
Banach Center Publications
We study a family of commuting selfadjoint operators , which satisfy, together with the operators of the family , semilinear relations , (, , are fixed Borel functions). The developed technique is used to investigate representations of deformations of the universal enveloping algebra U(so(3)), in particular, of some real forms of the Fairlie algebra .
Marcin Moszyński (2009)
Studia Mathematica
We prove that the absolutely continuous part of the periodic Jacobi operator does not change (modulo unitary equivalence) under additive perturbations by compact Jacobi operators with weights and diagonals defined in terms of the Stolz classes of slowly oscillating sequences. This result substantially generalizes many previous results, e.g., the one which can be obtained directly by the abstract trace class perturbation theorem of Kato-Rosenblum. It also generalizes several results concerning perturbations...
William Norrie Everitt (1986)
Časopis pro pěstování matematiky
Giuseppe Da Prato, Luciano Tubaro (2001)
Czechoslovak Mathematical Journal
Given a Hilbert space with a Borel probability measure , we prove the -dissipativity in of a Kolmogorov operator that is a perturbation, not necessarily of gradient type, of an Ornstein-Uhlenbeck operator.
T.H. Wolff, S.Y.A. Chang, J.M. Wilson (1985)
Commentarii mathematici Helvetici
Jan Janas, Marcin Moszyński (2012)
Studia Mathematica
We describe the spectra of Jacobi operators J with some irregular entries. We divide ℝ into three “spectral regions” for J and using the subordinacy method and asymptotic methods based on some particular discrete versions of Levinson’s theorem we prove the absolute continuity in the first region and the pure pointness in the second. In the third region no information is given by the above methods, and we call it the “uncertainty region”. As an illustration, we introduce and analyse the OP family...
Werner J. Ricker (1985)
Czechoslovak Mathematical Journal
S. Kantorovitz, R. J. Hughes (1988)
Mathematische Annalen
Klaus Kalb (1972)
Manuscripta mathematica
Karel Najzar (1970)
Commentationes Mathematicae Universitatis Carolinae
Jílek, Martin (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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