Publisher DOI: 10.4064/ap190728-17-11
arXiv ID: 1809.06457v4
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)
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
Journal: Annales Polonici mathematici 
Institute: Mathematik E-10 
Document Type: Article
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