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On weighted inductive limits of spaces of ultradifferentiable functions and their duals

Journal Contribution - Journal Article

In the first part of this paper we discuss the completeness of two general classes of weighted inductive limits of spaces of ultradifferentiable functions. In the second part we study their duals and characterize these spaces in terms of the growth of convolution averages of their elements. This characterization gives a canonical way to define a locally convex topology on these spaces and we give necessary and sufficient conditions for them to be ultrabornological. In particular, our results apply to spaces of convolutors for Gelfand–Shilov spaces.
Journal: MATHEMATISCHE NACHRICHTEN
ISSN: 0025-584X
Issue: 3
Volume: 292
Pages: 573 - 602
Publication year:2019
BOF-keylabel:yes
IOF-keylabel:yes
BOF-publication weight:0.1
CSS-citation score:2
Authors:National
Authors from:Higher Education
Accessibility:Closed