Abstract:
The discrete spectrumof selfadjoint operators in the Friedrichs model is studied. Necessary and sufficient conditions of existence of infinitely many eigenvalues in the Friedrichs model are presented. A discrete spectrum of a model three-particle discrete Schrödinger operator is described.
\Bibitem{Esh11}
\by Yu.~Kh.~Eshkabilov
\paper On infinity of the discrete spectrum of operators in the Friedrichs model
\jour Mat. Tr.
\yr 2011
\vol 14
\issue 1
\pages 195--211
\mathnet{http://mi.mathnet.ru/mt212}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2858663}
\elib{https://elibrary.ru/item.asp?id=16441661}
\transl
\jour Siberian Adv. Math.
\yr 2012
\vol 22
\issue 1
\pages 1--12
\crossref{https://doi.org/10.3103/S1055134412010014}
Linking options:
https://www.mathnet.ru/eng/mt212
https://www.mathnet.ru/eng/mt/v14/i1/p195
This publication is cited in the following 9 articles:
D. Zh. Kulturaev, Yu. Kh. Eshkabilov, “On the Spectral Properties of Selfadjoint Partial Integral Operators with a Nondegenerate Kernel”, Sib Math J, 65:2 (2024), 475
Yu. Kh. Eshkabilov, D. J. Kulturaev, “On discrete spectrum of one two-particle lattice Hamiltonian”, Ufa Math. J., 14:2 (2022), 97–107
G. P. Arzikulov, Yu. Kh. Eshkabilov, “About the spectral properties of one three-partial model operator”, Russian Math. (Iz. VUZ), 64:5 (2020), 1–7
R. R. Kucharov, Yu. Kh. Eshkabilov, “On the number of negative eigenvalues of a partial integral operator”, Siberian Adv. Math., 25:3 (2015), 179–190
G. P. Arzikulov, Yu. Kh. Eshkabilov, “On the essential and the discrete spectra of a Fredholm type partial integral operator”, Siberian Adv. Math., 25:4 (2015), 231–242
Yu. Kh. Eshkabilov, “On the discrete spectrum of partial integral operators”, Siberian Adv. Math., 23:4 (2013), 227–233
Eshkabilov Yu.Kh., “O beskonechnosti chisla otritsatelnykh sobstvennykh znachenii modeli Fridriskha”, Nanosistemy: fizika, khimiya, matematika, 3:6 (2012), 16–24
Boitsev A.A., Popov I.Yu., Sokolov O.V., “Gamiltonian s tochechnymi potentsialami i beskonechnym chislom sobstvennykh znachenii”, Nanosistemy: fizika, khimiya, matematika, 3:4 (2012), 9–19
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