The relevance of waves in quantum mechanics naturally implies that the decomposition of arbitrary wave packets in terms of monochromatic waves plays an important role in applications of the theory. When eigenfunction expansions does not converge, then the expansions of the functions with certain smoothness should be considered. Such functions gained prominence primarily through their application in quantum mechanics. Although today the function with certain singularity are also commonly used in mechanics and electrodynamics to describe sudden impulses, mass points, or point charges. In this work we study the almost everywhere convergence of the eigenfunctione expansions from Liouville classes \(L_{p}^{\alpha}(T^{N})\), related to the self-adjoint extension of the Laplace operator in torus \(T^{N}\). The sufficient conditions for summability is obtained using the modified Poisson formula. Isomorphism properties of the elliptic differential operators is applied in order to obtain estimation for the Fourier series of the functions from the classes of Liouville \(L_{p}^{\alpha}\).