Scientific reports of Bukhara State University


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


Last Page



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

Included in

Life Sciences Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.