Hardy’s Theorem and the Short-time Fourier Transform of Schwartz Functions
نویسندگان
چکیده
We characterize the Schwartz space of rapidly decaying test functions by the decay of the short-time Fourier transform or cross-Wigner distribution. Then we prove a version of Hardy’s theorem for the short-time Fourier transform and for the Wigner distribution.
منابع مشابه
An Analogue of Hardy’s Theorem for Very Rapidly Decreasing Functions on Semi-simple Lie Groups
A celebrated theorem of L. Schwartz asserts that a function f on R is ‘rapidly decreasing’ (or in the ‘Schwartz class’) iff its Fourier transform is ‘rapidly decreasing’. Since this theorem is of fundamental importance in harmonic analysis, there is a whole body of literature devoted to generalizing this result to other Lie groups. (For example, see [18].) In sharp contrast to Schwartz’s theore...
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