2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127767We prove an analogue of Gutzmer's formula for Hermite expansions. As a consequence we obtain a new proof of a characterisation of the image of $ L^2(\R^n) $ under the Hermite semigroup. We also obtain some new orthogonality relations for complexified Hermite functions.15 pagesClassical Analysis and ODEsFunctional Analysis42A38text