On the nuclearity of weighted spaces of smooth functions
Volume 124 / 2020
Annales Polonici Mathematici 124 (2020), 173-196
MSC: Primary 46A11; Secondary 46E10.
DOI: 10.4064/ap190728-17-11
Published online: 31 January 2020
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 $\mathcal {EV}(\Omega )$ of smooth functions on an open subset $\Omega \subset \mathbb R ^{d}$ whose topology is given by a family $\mathcal {V}$ of weights. We derive sufficient conditions on the weights to make $\mathcal {EV}(\Omega )$ a nuclear space.
