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

Snježana Maksimović; Sanja Atanasova; Zoran D. Mitrović; Salma Haque; Nabil Mlaiki; Snježana Maksimović; Sanja Atanasova; Zoran D. Mitrović; Salma Haque; Nabil Mlaiki

doi:10.3934/math.2024597

AIMS Mathematics

2024, Volume 9, Issue 5: 12225-12238. doi: 10.3934/math.2024597

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Research article

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

1.
Faculty of Architecture, Civil Engineering and Geodesy, University of Banja Luka, Stepe Stepanovića, 77/3, Banja Luka 78000, Bosnia and Hercegovina
2.
Faculty of Electrical Engineering and Information Technologies, Ss. Cyril and Methodius University in Skopje, Rugjer Boshkovik 18, Skopje 1000, North Macedonia
3.
Faculty of Electrical Engineering, University of Banja Luka, Patre 5, Banja Luka 78000, Bosnia and Herzegovina
4.
Department of Mathematics and Sciences, Prince Sultan University, 66833 Rafha Street, Riyadh 11586, Saudi Arabia

Received: 04 January 2024 Revised: 13 March 2024 Accepted: 25 March 2024 Published: 28 March 2024
MSC : 40E05, 43A50, 46F10, 46F12

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.
- fractional Fourier cosine (sine) transform,
- distributions,
- Abelian and Tauberian theorems
Citation: Snježana Maksimović, Sanja Atanasova, Zoran D. Mitrović, Salma Haque, Nabil Mlaiki. Abelian and Tauberian results for the fractional Fourier cosine (sine) transform[J]. AIMS Mathematics, 2024, 9(5): 12225-12238. doi: 10.3934/math.2024597

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Abstract

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.

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