Representing systems of exponentials in projective limits of weighted subspaces of

Abstract

We consider uniformly weighted spaces of analytic functions on a bounded convex domain in the complex plane with convex weights. For every uniformly weighted normed space we define a special inductive limit of normed spaces and a special projective limit of normed spaces. We prove that is the smallest locally convex space which contains and is invariant under differentiation, and is the largest such space which is contained in . We construct a representing system of exponentials in the projective limit and estimate the redundancy of this system.