Preview

Nanosystems: Physics, Chemistry, Mathematics

Advanced search

Non-compact perturbations of the spectrum of multipliers given with functions

https://doi.org/10.17586/2220-8054-2021-12-2-135-141

Abstract

The change in the spectrum of the multipliers H0 f (x, y) = xa + ye f (x, y) and H0f (x, y) = xaye f (x, y) for perturbation with partial integral operators in the spaces L2 [0, 1]2 is studied. Precise description of the essential spectrum and the existence of simple eigenvalue is received. We prove that the number of eigenvalues located below the lower edge of the essential spectrum in the model is finite.

About the Authors

R. R. Kucharov
National University of Uzbekistan
Uzbekistan

100174, Tashkent



R. R. Khamraeva
National University of Uzbekistan; Westminster International University in Tashkent
Uzbekistan

100174, Tashkent,

100010, 12, Istiqbol str., Tashkent



References

1. Uchiyama J. Finiteness of the Number of Discrete Eigenvalues of the Schrodinger Operator for a Three Particle System. 1969, Publ. Res. Inst. Math. Sci., 5 (1), P. 51–63.

2. Uchiyama J. Corrections to ”Finiteness of the Number of Discrete Eigenvalues of the Schrodinger Operator for a Three Particle System”. Publ. Res. Inst. Math. Sci., 1970, 6 (1), P. 189–192.

3. Uchiyama J. Finiteness of the Number of Discrete Eigenvalues of the Schrodinger Operator for a Three Particle System. Publ. Res. Inst. Math. Sci., 1970, 6 (1), P. 193–200.

4. Zhislin G.M. On the finiteness of the discrete spectrum of the energy operator of negative atomic and molecular ions. Theor. Math. Phys., 1971, 7, P. 571–578.

5. Appell J., Frolova E.V., Kalitvin A.S., Zabrejko P.P. Partial integral operators on C(a, b. × c, d.). Integral Equ. Oper. theory, 1997, 27, P. 125–140.

6. Faddeev L.D. On a model of Friedrichs in the theory of perturbations of the continuous spectrum. Trudy Mat. Inst. Steklov, 1964, 73, 292 in Russian..

7. Albeverio S., Lakaev S.N., Muminov Z.I. On the number of eigenvalues of a model operator associated to a system of three-particles on lattices. Russ. J. Math. Phys., 2007, 14 (4), P. 377—387.

8. Rasulov T.Kh. Asymptotics of the discrete spectrum of a model operator assotiated with a system of three particles on a lattice. Theor. and Math. Phys., 2010, 163 (1), P. 429–437.

9. Eshkabilov Yu.Kh., Kucharov R.R. Essential and discrete spectra of the three-particle Schrodinger operator on a lattice. Theor. Math. Phys., 2012, 170 (3), P. 341-–353.

10. Eshkabilov Yu.Kh., Kucharov R.R. Efimov’s effect for partial integral operators of Fredholm type. Nanosystems: Physics, Chemistry, Mathematics, 2013, 4 (4), P. 529–537.

11. Eshkabilov Yu.Kh. On infinity of the discrete spectrum of operators in the Friedrichs model. Siberian Adv. Math., 2012, 22 (1).

12. Reed M., Simon B. Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators, Acad. Press, New York, 1982.

13. Eshkabilov Yu.Kh. Efimov’s effect for a 3-particle model discrete Schrodinger operator. Theor. Math. Phys., 2010, 164 (1), P. 896-–904.

14. Eshkabilov Yu.Kh. On a discrete “three-particle” Schrodinger operator in the Hubbard model. Theor. Math. Phys., 2006, 149 (2), P. 1497–1511.


Review

For citations:


Kucharov R.R., Khamraeva R.R. Non-compact perturbations of the spectrum of multipliers given with functions. Nanosystems: Physics, Chemistry, Mathematics. 2021;12(2):135-141. https://doi.org/10.17586/2220-8054-2021-12-2-135-141

Views: 10


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 2220-8054 (Print)
ISSN 2305-7971 (Online)