Frames for Frechet spaces
given at strobl07 (17.06.07)
The motivation behind the present work comes from Banach frames and Xd-frames. During the last years, series expansions in a Banach space X and its dual X* via a Banach frame or an Xd-frame have been of interest.
In the present talk we extend the concept of a frame to Fr\'echet spaces. We consider family of Banach spaces and determine conditions, implying series expansions in their projective and inductive limit. The results are applicable to some important Fr\'echet spaces, for example the Schwartz class S of rapidly decreasing functions, which can be written as projective limit of certain modulation spaces.
The present work is joint with S. Pilipovic and N. Teofanov.