On spectral problems for nonlocal analogues of the polyharmonic operator


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Authors

  • V.V. Karachik Department of Mathematical Analysis, South Ural State University, 76 Lenin Ave, 454080 Chelyabinsk, Russian Federation
  • B.Kh. Turmetov Department of Mathematics, Kh.A. Yasawi International Kazakh-Turkish University, 29 B. Sattarhanov Ave, 161200 Turkistan, Republic of Kazakhstan

DOI:

https://doi.org/10.32523/2077-9879-2026-17-3-31-43

Keywords:

involution, nonlocal polyharmonic operator, boundary value problem, spectral problem, completeness

Abstract

In this paper, using mappings of the unit ball in \(\mathbb{R}^n\), associated with orthogonal matrices, two types of nonlocal analogues of the polyharmonic operator are introduced. Spectral problems for the Dirichlet problem and Dirichlet-type problems for these operators are studied. The eigenfunctions and eigenvalues of the problems under consideration are found. Theorems on the completeness of systems of eigenfunctions in the space \(L_2\) are proved.

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Published

2026-09-30

How to Cite

Karachik, V., & Turmetov, B. (2026). On spectral problems for nonlocal analogues of the polyharmonic operator. Eurasian Mathematical Journal, 17(3), 31–43. https://doi.org/10.32523/2077-9879-2026-17-3-31-43

Issue

Vol. 17 No. 3 (2026)

Section

Articles