Modulation Spaces, Multipliers Associated with the Special Affine Fourier Transform

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 M A r , s in connection with SAFT and prove that if a bounded linear operator between new modulation spaces commu...

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Veröffentlicht in:Complex analysis and operator theory 2022-09, Vol.16 (6), Article 86
Hauptverfasser: Biswas, M. H. A., Feichtinger, H. G., Ramakrishnan, R.
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Sprache:eng
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Zusammenfassung: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 M A r , s 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.
ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-022-01264-1