Holomorphic Sobolev spaces, Hermite ans special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

R. Radha, S. Thangavelu

The images of Hermite and Laguerre Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterised. These are used to characterise the Schwartz cla…