18 citations · 115 across the 44 of their papers we have counts for
48 papers
Some results about spaceability in function spaces
Andreas Debrouwere
We investigate two problems concerning spaceability in function spaces. First, we study the spaceability of sets of nowhere regular periodic functions, for various notions of regul…
Riesz summability of Dirichlet series generating holomorphic functions of finite order
Andreas Debrouwere, Yarne Tranoy
Given a frequency , we study the Riesz summability of -Dirichlet series generating holomorphic functions of finite order. We present a new…
Strong factorization theorem for smooth vectors of exponential solvable Lie group representations
Santiago Chaves, Andreas Debrouwere, Alberto Hernández Alvarado +2
We establish new strong factorization properties for the smooth vectors of representations of exponential solvable Lie groups on Fréchet spaces. In particular, our results improve…
A Pełczyński-Vogt decomposition result for (PLS)-spaces and sequence space representations
Andreas Debrouwere, Lenny Neyt
We establish a Pelczyński-Vogt decomposition result for (PLS)-type power series spaces of infinite type. By combining this result with the theory of Gabor frames, we obtain sequenc…
Sequence space representations of Beurling-Björck spaces via Gabor frames and Wilson bases
Andreas Debrouwere, Lenny Neyt
We establish sequence space representations of a broad class of Beurling-Björck spaces and . We develop two different approac…
A linear topological invariant for weighted spaces of holomorphic functions
Andreas Debrouwere, Quinten Van Boxstael
We study the linear topological invariant for a class of Fréchet spaces of holomorphic functions of rapid decay on strip-like domains in the complex plane, defined via weight…
Moment problems in the Schwartz and Gelfand-Shilov spaces
Andreas Debrouwere
We provide a geometric characterization of the closed sets such that every real -sequence is the moment sequence of some Schwartz function on $\mathbb…
On the surjectivity of the Cauchy-Riemann and Laplace operators on weighted spaces of smooth functions
Andreas Debrouwere, Quinten Van Boxstael, Jasson Vindas
We study the surjectivity of the Cauchy-Riemann and Laplace operators on certain weighted spaces of smooth functions of rapid decay on strip-like domains in the complex plane that…
Strong factorization of ultradifferentiable vectors associated with compact Lie group representations
Andreas Debrouwere, Michiel Huttener, Jasson Vindas
We show a strong factorization theorem of Dixmier-Malliavin type for ultradifferentiable vectors associated with compact Lie group representations on sequentially complete locally…
On the inclusion relations between Gelfand-Shilov spaces
Andreas Debrouwere, Lenny Neyt, Jasson Vindas
We study inclusion relations between Gelfand-Shilov type spaces defined via a weight (multi-)sequence system, a weight function system, and a translation-invariant Banach function…
Quasinormability and property for spaces of smooth and ultradifferentiable vectors associated with Lie group representations
Andreas Debrouwere, Michiel Huttener, Jasson Vindas
We prove that the spaces of smooth and ultradifferentiable vectors associated with a representation of a real Lie group on a Fréchet space are quasinormable if is so. A sim…
The vector-valued Stieltjes moment problem with general exponents
Andreas Debrouwere, Lenny Neyt
We characterize the sequences of complex numbers and the locally complete -spaces such that for each $(e_{n})_{n \in \mathbb{N}} \in E^\mathb…
An extension result for -spaces and the surjectivity of tensorized mappings
Andreas Debrouwere, Lenny Neyt
We study an extension problem for continuous linear maps in the setting of -spaces. More precisely, we characterize the pairs , where is a locally complete space w…
Linear topological invariants for kernels of differential operators by shifted fundamental solutions
Andreas Debrouwere, Thomas Kalmes
We characterize the condition for smooth kernels of partial differential operators in terms of the existence of shifted fundamental solutions satisfying certain properties. T…
Quantitative Runge type approximation theorems for zero solutions of certain partial differential operators
Andreas Debrouwere, Thomas Kalmes
We prove quantitative Runge type approximation results for spaces of smooth zero solutions of several classes of linear partial differential operators with constant coefficients. A…
A note on the barrelledness of weighted -spaces of ultradifferentiable functions
Andreas Debrouwere, Lenny Neyt
In this note we consider weighted -spaces of ultradifferentiable functions defined via a weight function and a weight system, as introduced in our previous work [4]. We prov…
Linear topological invariants for kernels of convolution and differential operators
Andreas Debrouwere, Thomas Kalmes
We establish the condition for smooth kernels of various types of convolution and differential operators. By the - splitting theorem of Vogt and Wagner, this impli…
A note on composition operators between weighted spaces of smooth functions
Andreas Debrouwere, Lenny Neyt
For certain weighted locally convex spaces and of one real variable smooth functions, we characterize the smooth functions for which the comp…
Sequence space representations for translation-modulation invariant function and distribution spaces
Andreas Debrouwere, Lenny Neyt
We provide sequence space representations for the test function space and the distribution space associated to a Banach space belon…
Explicit commutative sequence space representations of function and distribution spaces on the real half-line
Andreas Debrouwere, Lenny Neyt, Jasson Vindas
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 trans…
Sequence space representations for spaces of smooth functions and distributions via Wilson bases
Christian Bargetz, Andreas Debrouwere, Eduard A. Nigsch
We provide explicit sequence space representations for the test function and distribution spaces occurring in the Valdivia-Vogt structure tables by making use of Wilson bases gener…
Gabor frame characterisations of generalised modulation spaces
Andreas Debrouwere, Bojan Prangoski
We obtain Gabor frame characterisations of modulation spaces defined via a class of translation-modulation invariant Banach spaces of distributions that was recently introduced in…
Quasianalytic functionals and ultradistributions as boundary values of harmonic functions
Andreas Debrouwere, Jasson Vindas
We study boundary values of harmonic functions in spaces of quasianalytic functionals and spaces of ultradistributions of non-quasianalytic type. As an application, we provide a ne…
Boundary values of zero solutions of hypoelliptic differential operators in ultradistribution spaces
Andreas Debrouwere, Thomas Kalmes
We study ultradistributional boundary values of zero solutions of a hypoelliptic constant coefficient partial differential operator on . Our…