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Uniqueness theorem and singular spectrum in the Friedrichs model near a singular point
Author(s):
S.
I.
Yakovlev
Translated by:
the author
Original publication:
Algebra i Analiz,
tom 15
(2003),
vypusk 1.
Journal:
St. Petersburg Math. J.
15
(2004),
149-164.
MSC (2000):
Primary 47B06, 47B25
Posted:
December 31, 2003
MathSciNet review:
1979723
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References |
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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.
References:
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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:
10.1090/S1061-0022-03-00807-0
PII:
S 1061-0022(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):
19/JUN/2002
Posted:
December 31, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
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