Holomorphic Sobolev Spaces, Hermite and Special Hermite Semigroups and a Paley-wiener Theorem for the Windowed Fourier Transform
نویسنده
چکیده
The images of Hermite and Laguerre Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterised. These are used to characterise the image of Schwartz class of rapidly decreasing functions f on Rn and Cn under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for windowed ( short-time) Fourier transform is proved.
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