An analogue of Gutzmer's formula for Hermite expansions

Details An analogue of Gutzmer's formula for Hermite expansions An analogue of Gutzmer's formula for Hermite expansions

2007-04-21

arxiv.org/abs/0704.2834v1

Mathematics

Classical Analysis and ODEs

15 pages

Scientific paper

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(\R^n) $ under the Hermite semigroup. We also obtain some new orthogonality
relations for complexified Hermite functions.

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