9 citations · 9 across the 1 of their papers we have counts for
8 papers
Beurling integers with RH and large oscillation
Frederik Broucke, Gregory Debruyne, Jasson Vindas
We construct a Beurling generalized number system satisfying the Riemann hypothesis and whose integer counting function displays extremal oscillation in the following sense. The pr…
An asymptotic analysis of the Fourier-Laplace transforms of certain oscillatory functions
Frederik Broucke, Gregory Debruyne, Jasson Vindas
We study the family of Fourier-Laplace transforms $$ F_{α,β}(z)= \operatorname*{F.p.} \int_{0}^{\infty} t^β\exp(\mathrm{i} t^α-\mathrm{i} z t)\:\mathrm{d} t, \quad \operatorname*{I…
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…
Halász's theorem for Beurling generalized numbers
Gregory Debruyne, Frederick Maes, Jasson Vindas
We show that Halász's theorem holds for Beurling numbers under the following two mild hypotheses on the generalized number system: existence of a positive density for the generaliz…
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…