A Note on Generalized Frame Potential

Abstract

The concept of the frame potential was defined by Benedetto and Fickus [1] and it was showed that the finite unit norm tight frames can be characterized as the minimizers of the the energy functional. The concept was generalized by Carrizo and Heineken [5] and they introduced the concept of mixed frame potential. In the present paper, we further generalize the concept introducing the notion of generalized frame potential and observe that frame potential and mixed frame potential are particular cases of generalized frame potential. We prove some results concerning the generalized frame potential.

Key words and phrases. Frames, frame potential, finite dimensional Hilbert spaces.

2010 Mathematics Subject Classification. 42C15