Frames for Fréchet spaces

S. Pilipović, Diana Stoeva, N. Teofanov

In this paper we study frame representations in projective and inductive limits of Banach spaces. We introduce the notion of a Fréchet pre-frame for a given Fréchet space with respect to a Fréchet sequence space. Main results of the paper include the use of density arguments and representations in the case of projective limits of isomorphic reflexive Banach spaces. Examples based on modulation spaces, Sobolev type spaces and Kothe type spaces are given.