A sequence space representation of L. Schwartz’ space $${{\mathcal{O}_{C}}}$$

Abstract

We derive a representation of the isomorphic spaces \({\mathcal{O}_{C}}\) of very slowly increasing functions and \({\mathcal{O}_{M}'}\) of very rapidly decreasing distributions as a completed topological tensor product of sequence spaces. In order to describe this completed topological tensor product as a space of double sequences, we construct a representation as an inductive limit of vector valued sequence spaces. Moreover we compare the representations of \({\mathcal{O}_{C}}\) and \({\mathcal{O}_{M}}\) .