Аннотация
This paper investigates a multidimensional initial-boundary value problem for a nonlocal analogue of a hyperbolic equation with spatial nonlocal operators and nonlocal boundary conditions generated by a group of involutions. The method is based on representing the solution space as a direct sum of invariant subspaces, which makes it possible to reduce the original problem to a system of classical Dirichlet, Neumann, and Robin problems. The existence and uniqueness of a classical solution are proved, and the solution is constructed in the form of a Fourier series.