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Vol. 51 No. 2 (2025)
Serdica Mathematical Journal

Articles

p-Hyperbolic Zolotarev functions in boundary value problems for a p th order differential operator

https://doi.org/10.55630/serdica.2025.51.153-188

Published 20-10-2025

  • Michail F. Bessmertnyĭ
    • ,
  • Vladimir A. Zolotarev

Michail F. Bessmertnyĭ
V. N. Karazin Kharkov National University

Vladimir A. Zolotarev
B. Verkin Institute for Low Temperature Physics and Engineering and V. N. Karazin Kharkov National University

Abstract

For the self-adjoint operator of the pth derivative, a system of fundamental solutions is constructed. This system is analogues to the classical system of sines and cosines. The properties of such functions are studied. Classes of self-adjoint boundary conditions are
described. For the operator of the third derivative, the resolvent is calculated and an orthonormal basis of eigenfunctions is given.

2020 Mathematics Subject Classification:

34L10, 33B99

Keywords

boundary value problem, self-adjointness, operator resolvent, fundamental system of solutions

Full text

Author Details

Michail F. Bessmertnyĭ

Department of Physics
V. N. Karazin Kharkov National University
4 Svobody Sq, Kharkov, 61077, Ukraine
e-mail: bezsmermf@gmail.com

Vladimir A. Zolotarev

B. Verkin Institute for Low Temperature Physics
and Engineering
National Academy of Sciences of Ukraine
47 Nauky Ave., Kharkiv, 61103, Ukraine
and
Department of Higher Mathematics and Informatics
V. N. Karazin Kharkov National University
4 Svobody Sq, Kharkov, 61077, Ukraine
e-mail: vazolotarev@gmail.com

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