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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 2, Pages 400–415
(Mi smj2206)
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This article is cited in 4 scientific papers (total in 4 papers)
On the number of eigenvalues of a matrix operator
T. Kh. Rasulov Bukhara State University, Bukhara, Uzbekistan
Abstract:
We consider a matrix operator $H$ in the Fock space. We prove the finiteness of the number of negative eigenvalues of $H$ if the corresponding generalized Friedrichs model has the zero eigenvalue ($0=\min\sigma_\mathrm{ess}(H)$). We also prove that $H$ has infinitely many negative eigenvalues accumulating near zero (the Efimov effect) if the generalized Friedrichs model has zero energy resonance. We obtain asymptotics for the number of negative eigenvalues of $H$ below $z$ as $z\to-0$.
Keywords:
Efimov effect, Fock space, zero energy resonance, Hilbert–Schmidt class, Birman–Schwinger principle, discrete spectrum.
Received: 15.04.2010
Citation:
T. Kh. Rasulov, “On the number of eigenvalues of a matrix operator”, Sibirsk. Mat. Zh., 52:2 (2011), 400–415; Siberian Math. J., 52:2 (2011), 316–328
Linking options:
https://www.mathnet.ru/eng/smj2206 https://www.mathnet.ru/eng/smj/v52/i2/p400
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Abstract page: | 466 | Full-text PDF : | 84 | References: | 45 | First page: | 7 |
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