Frame Potentials and Orthogonal Vectors

2019/02/25 by Park, Josiah
#42C15 #43A90 #51Fxx #74G65 #80M50 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1902.09443

Abstract

An extension is given of a recent result of Glazyrin, showing that an orthonormal basis \e_i\_i=1^d joined with the vectors \e_j\_j=1^m, where 1≤ m < d minimizes the p-frame potential for p∈[1,2log(2m+1)/(2m)/log(m+1)/(m)] over all collections of N=d+m vectors \x₁,…,x_N \ in \mathbbS^d-1.

Related

• Frame potentials and the geometry of frames
• Universal optimal configurations for the p-frame potentials
• Frames on Krein Spaces
• Hamiltonians generated by Parseval frames
• Critical Pairs of Sequences of a Mixed Frame Potential