Duals of controlled K-g-frames and some equalities

Controlled frames for spherical wavelets were introduced to get a numerically more efficient approximation algorithm. The notion of K-frames has been introduced to study atomic systems with respect to a bounded linear operator K on a Hilbert space H. In this paper motivating the concept of duals of controlled and Kframes, the concept of controlled K-g-dual pair and dual operator are introduced and some known equalities and inequalities satisfied with duals are presented. The applications of these duals are in signal and Image processing.

Keywords:

Controlled g-frame , controlled K-g-frame , duals of controlled K-g-frames