Asymptotic analysis of generalized functions through some generalized integral transforms and frames

Generalized asymptotics is an important research subject that has attracted 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 generalized integral transform and its inverse. Another way to consider the asymptotic behavior of distributions is also through frames. Some Abelian- and Tauberian-type results for the quasiasymptotics of tempered distributions through the asymptotic behavior of generalized directional short-time Fourier transform and localized frames are presented. Also, several Abelian- and Tauberian-type results for the quasiasymptotics of Lizorkin distributions through the asymptotic behavior of generalized Stockwell and wavelet transforms are given.