|Publisher URL:||http://arxiv.org/abs/1809.06457v4||Publisher DOI:||10.4064/ap190728-17-11||Title:||On the nuclearity of weighted spaces of smooth functions||Language:||English||Authors:||Kruse, Karsten||Keywords:||Nuclear;Partition of unity;Smooth;Weight;Mathematics - Functional Analysis;Mathematics - Functional Analysis;46A11, 46E10||Issue Date:||2020||Source:||Annales Polonici Mathematici 2 (124): 173-196 (2020)||Journal or Series Name:||Annales Polonici mathematici||Abstract (english):||Nuclearity plays an important role for the Schwartz kernel theorem to hold and in transferring the surjectivity of a linear partial differential operator from scalar-valued to vector-valued functions via tensor product theory. In this paper we study weighted spaces 𝓔𝓥(Ω) of smooth functions on an open subset Ω⊂ℝᵈ whose topology is given by a family of weights 𝓥. We derive sufficient conditions on the weights which make 𝓔𝓥(Ω) a nuclear space.||URI:||http://hdl.handle.net/11420/6166||ISSN:||1730-6272||Institute:||Mathematik E-10||Type:||(wissenschaftlicher) Artikel|
|Appears in Collections:||Publications without fulltext|
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