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The fractional short-time Fourier transform can be defined in the space of tempered distributions S'(R), exhibiting specific generalized asymptotic behaviors characterized by Abelian and Tauberian-type theorems. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

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September 6, 2023

Abelian and Tauberian results for the fractional Fourier and short-time Fourier transforms of distributions

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Abstract

ABSTRACTWe introduce the fractional short-time Fourier transform in S′(R) and provide generalized asymptotics for the fractional Fourier and the short-time Fourier transforms within S′(R). Abelian- and Tauberian-type results are given.KEYWORDS: Fractional Fourier transformfractional short-time Fourier transformdistributionsAbelian and Tauberian theoremsAMS CLASSIFICATIONS: 46F1246F1040E0543A50 AcknowledgmentsThis paper was supported by the project F10 of the Serbian Academy of Sciences and Arts and by the project 'Localization in the phase space: theoretical, numerical and practical aspects', No. 19.032/961-103/19 financed by MNRVOID Republic of Srpska.Disclosure statementNo potential conflict of interest was reported by the author(s).

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