On Eigenfunctions and Eigenvalues of a Nonlocal Laplace Operator with Multiple Involution

Abstract

We study the eigenfunctions and eigenvalues of the boundary value problem for the nonlocal Laplace equation with multiple involution. An explicit form of the eigenfunctions and eigenvalues for the unit ball are obtained. A theorem on the completeness of the eigenfunctions of the problem under consideration is proved.

Keywords

• nonlocal Laplace operator
• multiple involution
• Dirichlet problem
• eigenfunctions
• eigenvalues