Scientific reports of Bukhara State University
Abstract
In this paper in the Hilbert space a bounded self-adjoint Friedrichs model with rank two perturbation is considered. Number and location of the eigenvalues of are studied. An existence conditions of these eigenvalues are found. Under some conditions we prove that the lower (upper) bound of the essential spectrum of is either threshold eigenvalue or virtual level of .
First Page
31
Last Page
38
References
1. Friedrichs K.O. Uber die Spectralzerlegung einee Integral operators. Math. Ann.,115:1 1938. – Р. 249 272.
2. Friedrichs K.O. On the perturbation of continuous spectra. Comm. Pure Appl. Math.,1:4 1948. – Р. 361 406.
3. Faddeev L.D. Stroenie rezolventi operatora Shredingera sistemi trex chastits i zadacha rasseyaniya. Dokl. AN SSSR, 145:2. 1962. - S. 301 304.
4. Faddeev L.D. O modeli Fridrixsa v teorii vozmusheniy neprerivnogo spektra. TrudiMat. Ins-taANSSSR, 73. 1964. - S. 292 313.
5. Albeverio S., Lakaev S.N., Makarov K.A., Muminov Z.I. The threshold effects for the two-particle Hamiltonians in lattice. Comm. Math. Phys. 262. 2006. – Р. 91 115.
6. Albeverio S., Lakaev S.N., Muminov Z.I. Schrӧdinger operators on lattices. The Efimov effect and discrete spectrum asymptotics. Ann. Henri Poincare. 5. 2004. – Р. 743 772.
7. Abdullaev J.I., Lakaev S.N. Asimptotika diskretnogo spektra raznostnogo trexchastichnogo operatora Shredingera na reshetke. Teor. imat. fiz., 136:2. 2003.- S. 231 245.
8. Albeverio S., Lakaev S.N., Muminov Z.I. The threshold effects for a family of Friedrichs models under rank one perturbations. J. Math. Anal. Appl. 330. 2007. – Р. 1152 1168.
9. Albeverio S., Lakaev S.N., Djumanova R.Kh. The essential and discrete spectrum of a model operator associated to a system of three identical quantum particles. Rep. Math. Phys. 63:3. 2009. – Р. 359 380.
10. Rid M., Saymon B. Metodi sovremennoy matematicheskoy fiziki. T. 4, Analiz operatorov. - M.: Mir, 1982. - 426 s
Recommended Citation
Rasulov, Tulkin Husenovich and Bakhronov, Bekzod Islom ugli
(2020)
"THRESHOLD EIGENVALUES AND RESONANCES OF A FRIEDRICHS
MODEL WITH RANK TWO PERTURBATION,"
Scientific reports of Bukhara State University: Vol. 3
:
Iss.
3
, Article 3.
Available at:
https://uzjournals.edu.uz/buxdu/vol3/iss3/3