An analogue of Gutzmer's formula for Hermite expansions
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🧮 math.CA
math.FA
keywords
hermiteanalogueexpansionsformulagutzmerobtaincharacterisationcomplexified
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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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