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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…
Bornological LB-spaces and idempotent adjunctions
Jack Kelly, Lenny Neyt, Sven-Ake Wegner
The notion of an LB-space was introduced by Grothendieck in his 1953 thèse, referring to a countable colimit of Banach spaces taken within the category of locally convex topologica…
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…
Quantitative uncertainty principles for time-frequency Gaussian decay
Lenny Neyt, Joachim Toft, Jasson Vindas
For real symmetric positive definite matrices and , we characterize when a function satisfies \[ |f(x)| \lesssim e^{-(\frac12 - λ) \langle Ax, x\ra…
Optimal decay of semi-uniformly stable operator semigroups with empty spectrum
Morgan Callewaert, Lenny Neyt, Jasson Vindas
We show that it is impossible to quantify the decay rate of a semi-uniformly stable operator semigroup based on sole knowledge of the spectrum of its infinitesimal generator. More…
Weighted function spaces: convolutors, multipliers, and mollifiers
Lenny Neyt, Yoshihiro Sawano
We study smooth function spaces of Gelfand-Shilov type, with global behavior governed through a translation-invariant Banach function space and localized via a weight function syst…