A note on the barrelledness of weighted (PLB)-spaces of ultradifferentiable functions

2022/06/21 by Debrouwere, Andreas, Neyt, Lenny · 1 citation
#46A08 #46A13 #46A63 #46E10 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2206.10252

Abstract

In this note we consider weighted (PLB)-spaces of ultradifferentiable functions defined via a weight function and a weight system, as introduced in our previous work [4]. We provide a complete characterization of when these spaces are ultrabornological and barrelled in terms of the defining weight system, thereby improving the main Theorem 5.1 of [4]. In particular, we obtain that the multiplier space of the Gelfand-Shilov space Σ^r_s(ℝ^d) of Beurling type is ultrabornological, whereas the one of the Gelfand-Shilov space S^r_s(ℝ^d) of Roumieu type is not barrelled.

Cited by

• A Pełczyński-Vogt decomposition result for (PLS)-spaces and sequence space representations

Related

• Weighted (PLB)-spaces of ultradifferentiable functions and multiplier spaces
• On the solution of the Cauchy problem in the weighted spaces of Beurling ultradistributions
• Gelfand-Shilov spaces for extended Gevrey regularity
• Weighted function spaces: convolutors, multipliers, and mollifiers
• Characterizations of weighted BMO space and its application