An analogue of Gutzmer's formula for Hermite expansions
Volume 185 / 2008
Studia Mathematica 185 (2008), 279-290
MSC: Primary 42A38; Secondary 42B99, 43A90.
DOI: 10.4064/sm185-3-5
Abstract
We 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(\mathbb R^n)$ under the Hermite semigroup. We also obtain some new orthogonality relations for complexified Hermite functions.
