Modulation spaces, multipliers associated with the special affine Fourier transform

2022/07/08 by Md. Haider Ali Biswas, Biswas, M. H. A., H. G. Feichtinger +3
Mathematics · #42A38 #42B25 #42B35 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2207.03696

openalex publication_date 2022/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study some fundamental properties of the special affine Fourier transform (SAFT) in connection with the Fourier analysis and time-frequency analysis. We introduce the modulation space \boldsymbol M^r,s_A in connection with SAFT and prove that if a bounded linear operator between new modulation spaces commutes with A-translation, then it is a A-convolution operator. We also establish Hörmander multiplier theorem and Littlewood-Paley theorem associated with the SAFT.

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