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Uniqueness theorem and singular spectrum in the Friedrichs model near a singular point


Author: S. I. Yakovlev
Translated by: the author
Original publication: Algebra i Analiz, tom 15 (2003), nomer 1.
Journal: St. Petersburg Math. J. 15 (2004), 149-164
MSC (2000): Primary 47B06, 47B25
Published electronically: December 31, 2003
MathSciNet review: 1979723
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Abstract | References | Similar Articles | Additional Information

Abstract: A uniqueness theorem is proved for a class of analytic functions with positive imaginary part that admit representation in a special form. This theorem imposes some restrictions on the character of decay of these functions in the vicinity of their zeros. As an application, the density of the point spectrum and the singular continuous spectrum are described for selfadjoint operators in the Friedrichs model near a singular point.


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Additional Information

S. I. Yakovlev
Affiliation: Departamento de Matematicas, Universidad Simon Bolivar, Apartado Postal 89000 Caracas 1080-A, Venezuela
Email: iakovlev@mail.ru; serguei@usb.ve

DOI: http://dx.doi.org/10.1090/S1061-0022-03-00807-0
Keywords: Analytic functions, real roots, Hilbert transform, singular point, uniqueness theorem, Friedrichs model, singular spectrum, eigenvalues, measure, Lipschitz class
Received by editor(s): June 19, 2002
Published electronically: December 31, 2003
Article copyright: © Copyright 2003 American Mathematical Society