Asymptotic Analysis of Generalized Functions through Some Generalized Integral Transforms and Frames

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Pages: 7-14
DOI: https://doi.org/10.54664/DCCW7526

Abstract:

Generalized asymptotics is an important research subject that has attracted the attention of many authors in diverse areas. In recent years it has become common to analyze the asymptotic behavior of distributions through the asymptotic behavior of some integral transforms or frames. Some Abelian- and Tauberian-type results from Buralieva et al. (Funct. Anal. Appl. 53:3-10, 2019); Buralieva et al. (Chatzakou et al. (eds) Women in Analysis and PDE, in the series “Research Perspectives Ghent Analysis and PDE Center” Birkhäuser, Cham, 2024); Buralieva (Funct. Anal. Appl. 57(1):29-39, 2023); and Buralieva (Asian-Eur. J. Math., 2025) for the quasiasymptotics of tempered and Lizorkin distributions through the asymptotics of the appropriate integral transforms and frames are presented.

Keywords:

Quasiasymptotics, Stockwell transform, wavelet transform, directional short-time Fourier transform, frames, Abelian- and Tauberian-type results.

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