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On the space of ultradistributions vanishing at infinity
Andreas Debrouwere, Lenny Neyt, Jasson Vindas
We study the structural and linear topological properties of the space of ultradistributions vanishing at infinity (with respect to a weight fun…
Multiresolution expansions and wavelets in Gelfand-Shilov spaces
Stevan Pilipović, Dušan Rakić, Nenad Teofanov +1
We study approximation properties generated by highly regular scaling functions and orthonormal wavelets. These properties are conveniently described in the framework of Gelfand-Sh…
A multidimensional Tauberian theorem for Laplace transforms of ultradistributions
Lenny Neyt, Jasson Vindas
We obtain a multidimensional Tauberian theorem for Laplace transforms of Gelfand-Shilov ultradistributions. The result is derived from a Laplace transform characterization of bound…
Structural theorems for quasiasymptotics of ultradistributions
Lenny Neyt, Jasson Vindas
We provide complete structural theorems for the so-called quasiasymptotic behavior of non-quasianalytic ultradistributions. As an application of these results, we obtain descriptio…
Multidimensional Tauberian theorems for wavelet and non-wavelet transforms
Stevan Pilipović, Jasson Vindas
We study several Tauberian properties of regularizing transforms of tempered distributions with values in Banach spaces, that is, transforms of the form $M^{\mathbf{f}}_ϕ(x,y)=(\ma…