TY  - JOUR
AU  - Maksimović, Snježana
AU  - Atanasova, Sanja
AU  - Mitrović, Zoran D.
AU  - Haque, Salma
AU  - Mlaiki, Nabil
PY  - 2024
TI  - Abelian and Tauberian results for the fractional Fourier cosine (sine) transform
JO  - AIMS Mathematics
SP  - 12225
EP  - 12238
VL  - 9
IS  - 5
AB  - 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.
UR  - https://doi.org/10.3934/math.2024597
DO  - 10.3934/math.2024597