On the nuclearity of weighted spaces of smooth functions

摘要

abstract_textpNuclearity 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 epsilon V(Omega) of smooth functions on an open subset Omega subset of R-d whose topology is given by a family V of weights. We derive sufficient conditions on the weights to make epsilon V(Omega) a nuclear space./p/abstract_text