Skip to main content
SpringerLink
Log in

On the discrete spectrum of partial integral operators

  • Published:
Siberian Advances in Mathematics Aims and scope Submit manuscript

Abstract

We prove a theorem on the discrete spectrum of a partial integral selfadjoint operator with a continuous kernel.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Albeverio, S. N. Lakaev, and Z. I. Muminov, “On the number of eigenvalues of a model operator associated to a system of three-particles on lattices,” Russian J. Math. Phys. 14(4), 377–387 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  2. Yu. Kh. Eshkabilov, “Two electrons in the Hubbert model with admixture. Triplicate state,” Deposited by the Uzbekistan State Scientific Foundation on 08. 07. 1994, №2148-Uz94.

  3. Yu. Kh. Eshkabilov, “A discrete three-particle Schrödinger operator in the Hubbard model,” Teoret. i Mat. Fiz. 149(2), 228–243 (2006) [Theoret. and Math. Phys. 149 (2), 1497–1511 (2006)].

    Article  MathSciNet  Google Scholar 

  4. Yu. Kh. Eshkabilov, “Partially bounded operators with bounded kernels,” Matemat. Trudy 11(1), 192–207 (2008) [Siberian Adv. Math. 19 (3), 151–161].

    MathSciNet  MATH  Google Scholar 

  5. Yu. Kh. Eshkabilov, “The Efimov effect for a model three-particle discrete Schrödinger operator,” Teoret. i Matem. Fiz. 164(1), 78–87 (2010) [Theor. and Math. Phyz. 164 (1), 896–904 (2010)].

    Article  Google Scholar 

  6. Yu. Kh. Eshkabilov, “On infinity of the discrete spectrum of operators in the Friedrichsmodel,” Matem. Trudy 14(1), 195–211 (2011) [Siberian Adv. Math., 22 (1), 1–12 (2012)].

    MathSciNet  MATH  Google Scholar 

  7. Yu. Kh. Eshkabilov and R. R. Kucharov, “Essential and discrete spectra of the three-particle Schrödinger operator on a lattice,” Teoret. i Mat. Fiz, 170(3), 409–422 [Theoret. and Math. Phys. 170 (3), 341–353 (2012)].

  8. Yu. Kh. Eshkabilov and O. I. Sakhobidinova, “On infinity of the discrete spectrum of operators in the Friedrichs model,” in Mathematical forum (Scientific Results of South Russia); 1, Study on Mathematical Analysis (Vladikavkaz: VSC RAS, 2008), pp. 246–255 [in Russia].

    Google Scholar 

  9. Yu. Kh. Eshkabilov, “Spectra of partial integral operators with a kernel of three variables,” Central European J. Math., 6(1), 149–157 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  10. A. S. Kalitvin, “The spectrum of linear operators with partial integrals and positive kernels,” in Operators and their applications (Leningrad. Gos. Ped. Inst., Leningrad, 1988), pp. 43–50 [in Russian].

    Google Scholar 

  11. A. S. Kalitvin and P. P. Zabrejko, “On the theory of partial integral operators” J. Integral Equations Appl. 3(3), 351–382 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  12. L. M. Lihtarnikov and L. Z. Vitova, “The spectrum of a partial integral operator,” Litovsk. Mat. Sb., 15(2), 41–47, (1975) [in Russian].

    MathSciNet  MATH  Google Scholar 

  13. V. A. Malyshev and R. A. Minlos, “Cluster operators,” Trudy Sem. Petrovsk., 9, 63–80 (1983) [in Russian].

    MathSciNet  MATH  Google Scholar 

  14. D. C. Mattis “The few-body problem on a lattice,” Rev. Modern Phys. 58(2), 361–379 (1986).

    Article  MathSciNet  Google Scholar 

  15. A. I. Mogilner, “The problem of a few quasi-particles in solid-state physics,” Lecture Notes Phys. 324, Berlin: Springer-Verlag, 1988.

    Google Scholar 

  16. A. I. Mogilner, “Hamiltonians in solid-state physics as multiparticle discrete Schrödinger operators: problems and results,” Adv. Soviet Math., Providence, RI: Amer. Math. Soc., 5, 139–194 (1991).

    MathSciNet  Google Scholar 

  17. T. Kh. Rasulov, “Asymptotics of the discrete spectra of the model operator associated with a system of three particles on a lattice,” Teoret. i Matemat. Fiz. 163(1), 34–44 (2010). [Theoret. and Math. Phys. 163 (1), 429–437 (2010)].

    Article  MathSciNet  Google Scholar 

  18. M. Reed and B. Siman, Methods of Modern Mathematical Physics. Vol. I. Functional Analysis. (Academic Press Inc., N. Y., 1980).

    Google Scholar 

  19. V. I. Smirnov, Course of Higher Mathematics, Moscow: Nauka, Vol. 4,Part I, 1974 [in Russian].

    Google Scholar 

  20. Yu. V. Zhukov, “The Iorio-O’Carroll theorem for an N-particle letticeHamiltonian,” Teoret. iMatemat. Fiz., 107(1), 75–85 (1996) [Theoret. and Math. Phys., 107 (1), 478–486, (1996)].

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The National University of Uzbekistan, Tashkent, 100174, Uzbekistan

    Yu. Kh. Eshkabilov

Authors
  1. Yu. Kh. Eshkabilov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. Kh. Eshkabilov.

Additional information

Original Russian Text © Yu. Kh. Eshkabilov, 2012, published in Matematicheskie Trudy, 2012, Vol. 15, No. 2, pp. 194–203.

About this article

Cite this article

Eshkabilov, Y.K. On the discrete spectrum of partial integral operators. Sib. Adv. Math. 23, 227–233 (2013). https://doi.org/10.3103/S1055134413040019

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1055134413040019

Keywords

Search

Navigation