arXiv subjects

Lenny Neyt

Publications and source records attributed to Lenny Neyt.

28 records · Page 2Linked to original sources

arXiv2022

Weighted $(PLB)$-spaces of ultradifferentiable functions and multiplier spaces

We study weighted $(PLB)$-spaces of ultradifferentiable functions defined via a weight function (in the sense of Braun, Meise and Taylor) and a weight system. We characterize when such spaces are ultrabornological in terms of the defining weight system. This generalizes Grothendieck's classical result that the space $\mathcal{O}_M$ of slowly increasing smooth functions is ultrabornological to the context of ultradifferentiable functions. Furthermore, we determine the multiplier spaces of Gelfand-Shilov spaces and, by using the above result, characterize when such spaces are ultrabornological. In particular, we show that the multiplier space of the space of Fourier ultrahyperfunctions is ultrabornological, whereas the one of the space of Fourier hyperfunctions is not.

math.FA↗

arXiv2022

A lower bound for the life span of solutions to the Kirchhoff equation with Gevrey data

We provide a new lower bound for the life span of solutions to the Kirchhoff equation for which the initial data belongs to the Gevrey space. This lower bound strictly improves the classical one in the case when the frequency spectrum of the initial data is concentrated at the origin.

math.AP↗

arXiv2022

Explicit commutative sequence space representations of function and distribution spaces on the real half-line

We provide explicit commutative sequence space representations for classical function and distribution spaces on the real half-line. This is done by evaluating at the Fourier transforms of the elements of an orthonormal wavelet basis.

math.FA↗

arXiv2021

Convolutors of translation-modulation invariant Banach spaces of ultradistributions

We study the space of tempered ultradistributions whose convolutions with test functions are all contained in a given translation-modulation invariant Banach space of ultradistributions. Our main result will be the first structural theorem for the aforementioned space. As an application we consider several extensions of convolution.

math.FA↗

arXiv2021

Characterization of nuclearity for Beurling-Björck spaces

We characterize the nuclearity of the Beurling-Björck spaces $\mathcal{S}^{(ω)}_{(η)}(\mathbb{R}^d)$ and $\mathcal{S}^{\{ω\}}_{\{η\}}(\mathbb{R}^d)$ in terms of the defining weight functions $ω$ and $η$.

math.FA↗

arXiv2021

Asymptotic boundedness and moment asymptotic expansion in ultradistribution spaces

We obtain structural theorems for the so-called S-asymptotic and quasiasymptotic boundedness of ultradistributions. Using these results, we then analyze the moment asymptotic expansion (MAE), providing a full characterization of those ultradistributions satisfying this asymptotic formula in the one-dimensional case. We also introduce and study a uniform variant of the MAE.

math.FA↗

arXiv2020

The nuclearity of Gelfand-Shilov spaces and kernel theorems

We study the nuclearity of the Gelfand-Shilov spaces $\mathcal{S}^{(\mathfrak{M})}_{(\mathscr{W})}$ and $\mathcal{S}^{\{\mathfrak{M}\}}_{\{\mathscr{W}\}}$, defined via a weight (multi-)sequence system $\mathfrak{M}$ and a weight function system $\mathscr{W}$. We obtain characterizations of nuclearity for these function spaces that are counterparts of those for Köthe sequence spaces. As an application, we prove new kernel theorems. Our general framework allows for a unified treatment of the Gelfand-Shilov spaces $\mathcal{S}^{(M)}_{(A)}$ and $\mathcal{S}^{\{M\}}_{\{A\}}$ (defined via weight sequences $M$ and $A$) and the Beurling-Björck spaces $\mathcal{S}^{(ω)}_{(η)}$ and $\mathcal{S}^{\{ω\}}_{\{η\}}$ (defined via weight functions $ω$ and $η$). Our results cover anisotropic cases as well.

math.FA↗

arXiv2019

On the space of ultradistributions vanishing at infinity

We study the structural and linear topological properties of the space $\dot{\mathcal{B}}^{\prime \ast}_ω$ of ultradistributions vanishing at infinity (with respect to a weight function $ω$). Particularly, we show the first structure theorem for $\dot{\mathcal{B}}^{\prime \ast}_ω$ under weaker hypotheses than were known so far. As an application, we determine the structure of the S-asymptotic behavior of ultradistributions.

math.FA↗

arXiv2019

A multidimensional Tauberian theorem for Laplace transforms of ultradistributions

We obtain a multidimensional Tauberian theorem for Laplace transforms of Gelfand-Shilov ultradistributions. The result is derived from a Laplace transform characterization of bounded sets in spaces of ultradistributions with supports in a convex acute cone of $\mathbb{R}^{n}$, also established here.

math.FA↗

arXiv2018

Structural theorems for quasiasymptotics of ultradistributions

We provide complete structural theorems for the so-called quasiasymptotic behavior of non-quasianalytic ultradistributions. As an application of these results, we obtain descriptions of quasiasymptotic properties of regularizations at the origin of ultradistributions and discuss connections with Gelfand-Shilov type spaces.

math.FA↗