Kruse, KarstenKarstenKruse2020-05-182020-05-182020Annales Polonici Mathematici 2 (124): 173-196 (2020)http://hdl.handle.net/11420/6166Nuclearity 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.en1730-627220202173196NuclearPartition of unitySmoothWeightMathematics - Functional AnalysisMathematics - Functional Analysis46A11, 46E10Journal Article10.4064/ap190728-17-111809.06457v4Other