Tight p-fusion frames

TL;DR

This paper introduces p-fusion frames, a refined concept of fusion frames, and explores their properties and connections to designs and cubature formulas in Grassmann spaces using harmonic analysis.

Contribution

It defines the notion of p-fusion frames, introduces the p-fusion frame potential, and establishes bounds and relationships to classical mathematical structures.

Findings

Defined p-fusion frames and their properties

Derived bounds for the p-fusion frame potential

Connected tight p-fusion frames to designs in Grassmann spaces

Abstract

Fusion frames enable signal decompositions into weighted linear subspace components. For positive integers p, we introduce p-fusion frames, a sharpening of the notion of fusion frames. Tight p-fusion frames are closely related to the classical notions of designs and cubature formulas in Grassmann spaces and are analyzed with methods from harmonic analysis in the Grassmannians. We define the p-fusion frame potential, derive bounds for its value, and discuss the connections to tight p-fusion frames.