Skip to main content
SpringerLink
Log in

On the Discreteness of the Spectrum of Matrix Schrödinger and Dirac Operators with Point Interactions

  • Short Communications
  • Published:
Mathematical Notes Aims and scope Submit manuscript

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

References

  1. M. G. Krein, Dokl. AN SSSR 69 (2), 125 (1949).

    Google Scholar 

  2. Yu. M. Berezanskii, Expansions in Eigenfunctions of Self-Adjoint Operators (Naukova Dumka, Kiev, 1965) [in Russian].

    MATH  Google Scholar 

  3. A. G. Kostyuchenko and K. A. Mirzoev, Math. Notes 63 (5), 624 (1998).

  4. Yu. M. Dyukarev, Sb. Math. 201 (12), 1791 (2010).

    Article  MathSciNet  Google Scholar 

  5. A. S. Kostenko and M. M. Malamud, J. Differential Equations 249 (2), 253 (2010).

    Article  MathSciNet  Google Scholar 

  6. R. Carlone, M. Malamud, and A. Posilicano, J. Differential Equations 254 (9), 3835 (2013).

    Article  MathSciNet  Google Scholar 

  7. K. A. Mirzoev and T. A. Safonova, Math. Notes 99 (2), 290 (2016).

    Article  MathSciNet  Google Scholar 

  8. A. S. Kostenko, M. M. Malamud, and D. D. Natyagailo, Math. Notes 100 (1), 49 (2016).

    Article  MathSciNet  Google Scholar 

  9. I. N. Braeutigam and K. A. Mirzoev, St. Petersburg Math. J. 30 (4), 621 (2019).

    Article  MathSciNet  Google Scholar 

  10. V. Budyka, M. Malamud and A. Posilicano, Russ. J. Math. Phys. 24 (4), 426 (2017).

    Article  MathSciNet  Google Scholar 

  11. V. S. Budyka, M. M. Malamud, and A. Posilicano, Dokl. AN 479 (2), 117 (2018).

    Article  MathSciNet  Google Scholar 

  12. V. S. Budyka and M. M. Malamud, Math. Notes 106 (6), 1009 (2019).

    Google Scholar 

  13. V. S. Budyka and M. M. Malamud, Math. Notes 108 (3), 445 (2020).

    Google Scholar 

  14. P. A. Cojuhari and J. Janas, Acta Sci. Math. (Szeged) 73 (3), 649 (2007).

    Article  Google Scholar 

  15. J. Janas and S. Naboko, in Recent Advances in Operator Theory, Oper. Theory Adv. Appl. (Birkhäuser, Basel, 2001), Vol. 124, pp. 267–285.

    MathSciNet  Google Scholar 

  16. V. A. Derkach and M. M. Malamud, J. Funct. Anal. 95 (1), 1 (1991).

    Article  Google Scholar 

  17. F. Gesztesy and P. Šeba, Lett. Math. Phys. 13 (4), 345 (1987).

    Article  MathSciNet  Google Scholar 

  18. S. Albeverio, F. Gesztesy, R. Hoegh-Krohn, and H. Holden, Solvable Models in Quantum Mechanics (AMS Chelsea Publ., Providence, RI, 2005).

    Article  MathSciNet  Google Scholar 

Download references

Funding

This work was supported by the Ministry of Science and Higher Education of the Russian Federation within the framework of the state assignment: agreement no. 075-03-2020-223/3 (FSSF-2020-0018).

Author information

Authors and Affiliations

  1. Donetsk State Academy of Management and Public Administration, Donetsk, 83015, Ukraine

    V. S. Budyka

  2. Peoples’ Friendship University of Russia (RUDN University), Moscow, 117198, Russia

    V. S. Budyka & M. M. Malamud

Authors
  1. V. S. Budyka
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. M. Malamud
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. S. Budyka.

Additional information

Translated from Matematicheskie Zametki, 2021, Vol. 110, pp. 932–938 https://doi.org/10.4213/mzm13234.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Budyka, V.S., Malamud, M.M. On the Discreteness of the Spectrum of Matrix Schrödinger and Dirac Operators with Point Interactions. Math Notes 110, 960–966 (2021). https://doi.org/10.1134/S0001434621110341

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434621110341

Keywords

Search

Navigation