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Dirac Operators with Singular Potentials Supported on Unbounded Surfaces in \(\mathbb{R}^{3}\)

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Abstract

We consider the self-adjointness and essential spectrum of 3D Dirac operators with bounded variable magnetic and electrostatic potentials and with singular delta-type potentials with supports on uniformly regular unbounded surfaces \(\Sigma\) in \(\mathbb{R}^{3}\).

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References

  1. M. S. Agranovich and M. I. Vishik, Uspekhi Mat. Nauk, 19:3 (1964), 53–161; English transl.:, Russian Math. Surveys, 19:3 (1964), 53–157.

    MathSciNet  Google Scholar 

  2. H. Amman, Elliptic and Parabolic Equations, Springer Proceedings in Mathematics and Statistic, 119 Springer-Verlag, Hannover, 2013, 1–42.

    Google Scholar 

  3. N. Arrizabalaga, A. Mas, and L. Vega, Math. Pures Appl. (9), 102:4 (2014), 617–639.

    Article  MathSciNet  Google Scholar 

  4. J. Behrndt, P. Exner, M. Holzmann, and V. Lotoreichik, J. Math. Pures Appl., 111 (2018), 47–78.

    Article  MathSciNet  Google Scholar 

  5. J. Behrndt, P. Exner, M. Holzmann, and V. Lotoreichik, Quantum Stud. Math. Found., 6:3 (2019), 295–314.

    Article  MathSciNet  Google Scholar 

  6. M. Holzmann, Th. Ourmières-Bonafos, and K. Pankrashkin,, Rev. Math. Phys., 30:05 (2018).

    Article  MathSciNet  Google Scholar 

  7. A. Moroianu, Th. Ourmíeres-Bonafos, and K. Pankrashkin, J. Math. Pures Appl., 102:4 (2014), 617–639.

    Article  MathSciNet  Google Scholar 

  8. Th. Ourmieres-Bonafos and L. Vega, Publ. Mat., 62:3 (2018), 397–437.

    Article  MathSciNet  Google Scholar 

  9. V. S. Rabinovich, S. Roch, and B. Silbermann, Limit Operators and their Applications in Operator Theory, Operator Theory: Advances and Applications, 150 Birkhäuser, Basel–Boston–Berlin, 2004.

    Book  Google Scholar 

  10. V. S. Rabinovich, Russ. J. Math. Physics, 12:1 (2005), 62–80.

    MathSciNet  Google Scholar 

  11. V. S. Rabinovich, Appl. Anal., 94:10 (2015), 2077–2094.

    Article  MathSciNet  Google Scholar 

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Correspondence to V. S. Rabinovich.

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Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2021, Vol. 55, pp. 85–90 https://doi.org/10.4213/faa3838.

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Rabinovich, V.S. Dirac Operators with Singular Potentials Supported on Unbounded Surfaces in \(\mathbb{R}^{3}\). Funct Anal Its Appl 55, 245–249 (2021). https://doi.org/10.1134/S0016266321030084

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  • DOI: https://doi.org/10.1134/S0016266321030084

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