2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/218409The spectral theory of the Fourier operator (non-truncated) is expounded. The known construction of basis of eigenvectors consisting of the Hermite functions is presented. The detail description of the eigenspaces in the spirit of a work by Hardy and Titchmarsh is done.26 pagesClassical Analysis and ODEsSpectral Theory47A38 (Primary) 47B35, 47B06 (Secondary)text