Tame (PLS)-spaces

Abstract

The class of (PLS)-spaces covers most of the natural spaces of analysis, e. g. the space of real analytic functions, spaces of distributions. We characterize those (PLS)-spaces for which there exists a 'reasonable' (LFS)-topology, i. e. a topology of the inductive limit of a sequence of Fréchet-Schwartz spaces. Then we characterize - in terms of the defining sequence - power series (PLS)-type spaces which satisfy the same condition. It is known that power series (PLS)-type spaces appear naturally as kernels of convolution operators.