Abelian and Tauberian results for the fractional Fourier cosine (sine) transform

Journal
AIMS Mathematics
Date Issued
2024
Author(s)
Maksimović, Snježana
Mitrović, Zoran D.
Haque, Salma
Mlaiki, Nabil
DOI
10.3934/math.2024597
Abstract
<jats:p xml:lang="fr"><abstract><p>In this paper, we presented Tauberian type results that intricately link the quasi-asymptotic behavior of both even and odd distributions to the corresponding asymptotic properties of their fractional Fourier cosine and sine transforms. We also obtained a structural theorem of Abelian type for the quasi-asymptotic boundedness of even (resp. odd) distributions with respect to their fractional Fourier cosine transform (FrFCT) (resp. fractional Fourier sine transform (FrFST)). In both cases, we quantified the scaling asymptotic properties of distributions by asymptotic comparisons with Karamata regularly varying functions.</p></abstract></jats:p>
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