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Time-frequency analysis associated with the deformed Stockwell transform. (English) Zbl 1497.44005

Summary: In this paper, we consider the deformed Stockwell transform. Knowing the fact that the study of the time-frequency analysis are both theoretically interesting and practically useful, we investigated several problems for this subject on the setting of the deformed Stockwell transform. Firstly, we study the boundedness and compactness of localization operators associated with the deformed Stockwell transforms on \(\mathbb{R} \). Next, we present typical examples of localization operators. Finally, the scalogram for the deformed Stockwell transform are introduced and studied at the end.

MSC:

44A15 Special integral transforms (Legendre, Hilbert, etc.)
47G10 Integral operators
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
47G30 Pseudodifferential operators
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