On a Series of Eigen Functions

The eigenvalues are the numbers λ_n which are such that λ_n = n²₁ + n²₂ + n²_k, where n₁n₂,......, n_k are positive or negative integers or zero, and the associated eigenfunctions are ω_n, where ω_n = e^{i(n₁r₁+n₂r₂+......+n_kr_k)}.