Remark on the bounded non-self-adjoint friedrichs model
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Аннотация
In the present paper we consider the bounded, but not-self-adjoint Friedrichs model A with rank one perturbation. We show the for any positive integer number m there exist the parameter functions of the operator A such that this operator has at least
m eigenvalues.
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Библиографические ссылки
K.O. Friedrichs. Uber die Spectralzerlegung einee Integral operators. Math. Ann., –Berlin,
, –V.115, –№1, –P. 249-272.
K.O. Friedrichs. On the perturbation of continuous spectra. Comm. Pure Appl. Math., New
York, 1948, –V.1, –№4, –P. 361-406.
Zh.I. Abdullaev and S.N. Lakaev. On the Spectral Properties of the Matrix-Valued Friedrichs
Model. Many-particle Hamiltonians: spectra and scattering. Adv. Sov. Math., AMS., Providence
RI, 5 (1991), pp. 1–37.
I.A. Ikromov and F. Sharipov. On the Discrete Spectrum of the Nonanalytic Matrix-Valued
Friedrichs Model. Func. Anal. Appl., 32 (1998), no. 1, pp. 49–51.
M.I. Muminov. Expression for the Number of Eigenvalues of a Friedrichs Model. Math. Notes,
:1 (2007), pp. 67–74.