Asymptotic relations for some generalized integral transforms and frames

Asymptotic analysis of distributions is a very attractive research field that took the attention of different authors. In the recent years it has become common to analyze the asymptotic behavior of distributions through the asymptotic behavior of some generalized integral transforms and 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, polynomial multiplication of Lizorkin distributions and m-th derivative Lizorkin distributions in terms of their generalized Stockwell and wavelet transforms are given. Some asymptotic results for both transforms of the m-th derivative of Dirac delta distribution are given.