Constructing infinite tight frames

Abstract

Abstract. For finite and infinite dimensional Hilbert spaces H we classify the sequences of positive real numbers {an} ∞ n=1 so that there is a tight frame {ϕn} ∞ n=1 for H satisfying: ‖ϕn ‖ = an, for all n = 1, 2, 3, · · ·. In the finite dimensional case we will identify the frames which are closest to being tight (in the sense of minimizing potential enerty) for any sequence {an} ∞ n=1. 1