We show that the Gelfand-Shilov algebra S^{1/2}_{1/2} is densely embedded in the weighted modulation space M^1_m. Here the weight function m is allowed to have a super-exponential growth at infinity. The basic tool is given by an integral transform called short-time Fourier transform (STFT). The STFT is used to both define and characterize the previous spaces. Moreover, our result is attained using the properties of the STFT and its adjoint.
Gelfand-Shilov Window Classes for Weighted Modulation Spaces.
CORDERO, Elena
2007-01-01
Abstract
We show that the Gelfand-Shilov algebra S^{1/2}_{1/2} is densely embedded in the weighted modulation space M^1_m. Here the weight function m is allowed to have a super-exponential growth at infinity. The basic tool is given by an integral transform called short-time Fourier transform (STFT). The STFT is used to both define and characterize the previous spaces. Moreover, our result is attained using the properties of the STFT and its adjoint.
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