On the nuclearity of weighted spaces of smooth functions

Publikationstyp
Journal Article
Publikationsdatum
2020
Sprache
English
Author
Kruse, Karsten orcid-logo
Institut
Mathematik E-10 
TORE-URI
http://hdl.handle.net/11420/6166
Enthalten in
Annales Polonici mathematici 
Volume
124
Issue
2
Start Page
173
End Page
196
Citation
Annales Polonici Mathematici 2 (124): 173-196 (2020)
Publisher DOI
10.4064/ap190728-17-11
Scopus ID
2-s2.0-85084373973
ArXiv ID
1809.06457v4
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 ๐“”๐“ฅ(ฮฉ) of smooth functions on an open subset ฮฉโŠ‚โ„แตˆ whose topology is given by a family of weights ๐“ฅ. We derive sufficient conditions on the weights which make ๐“”๐“ฅ(ฮฉ) a nuclear space.
Schlagworte
Nuclear
Partition of unity
Smooth
Weight
Mathematics - Functional Analysis
Mathematics - Functional Analysis
46A11, 46E10