Construction of Eigenfunctions to One Nonlocal Second-Order Differential Operator with Double Involution

Abstract

In this paper, we study the eigenfunctions to one nonlocal second-order differential operator with double involution. We give an explicit form of the eigenfunctions to the boundary value problem in the unit ball with Dirichlet conditions on the boundary. For the problem under consideration, the completeness of the system of eigenfunctions is established.

Keywords

• nonlocal differential operator
• double involution
• boundary value problem
• eigenfunctions
• eigenvalues