A representation-theoretic deformation of the Fourier transform and partial derivatives on R^N that interchanges them via F_b while preserving an sl(2) structure and providing a smooth analogue of Dunkl operators.
The oscillator semigroup
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A Generalized Fourier Transform and a Smooth Analogue of Dunkl Operators
A representation-theoretic deformation of the Fourier transform and partial derivatives on R^N that interchanges them via F_b while preserving an sl(2) structure and providing a smooth analogue of Dunkl operators.