On the nuclearity of weighted spaces of smooth functions

Karsten Kruse

doi:10.4064/ap190728-17-11

On the nuclearity of weighted spaces of smooth functions

Karsten Kruse^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

4 Citations (Scopus)

Abstract

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 ⊂ R^d whose topology is given by a family V of weights. We derive sufficient conditions on the weights to make EV(Ω) a nuclear space.

Original language	English
Pages (from-to)	173-196
Number of pages	24
Journal	Annales Polonici Mathematici
Volume	124
Issue number	2
DOIs	https://doi.org/10.4064/ap190728-17-11
Publication status	Published - 2020
Externally published	Yes

Keywords

Nuclear
Partition of unity
Smooth
Weight
NLA

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On the nuclearity of weighted spaces of smooth functions

Abstract

Keywords

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