Operational methods and solutions of boundary-value problems with periodic data

We introduce suitable exponential operators and use the multi-dimensional polynomials considered by Hermite and subsequently studied by P. Appell and J. Kampé de Fériet, H. W. Gould and A. T. Hopper, and G. Dattoli et al. in order to obtain explicit solutions of classical boundary-value problems with periodic data. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 51, Differential Equations and Their Applications, 2008.