Frame Potential in CPn  Some Numerical and Analytical Results

Radel Ben Av; Giora Dula; Assaf Goldberger; Yossi Strassler

doi:10.1080/10586458.2020.1753597

Frame Potential in CPⁿ Some Numerical and Analytical Results

Radel Ben Av^*, Giora Dula, Assaf Goldberger, Yossi Strassler

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we discuss minimizing a generalized frame potential - F(p,m,n) - for vectors in CPⁿ. We discuss the minimal frame potential as well as the space of solutions for the minimization problem. We investigate this question both numerically and analytically. We find that for some values of p - Equiangular Tight Frames (ETF) are unique solutions, in contrast to the case of p = 2 where they are non-unique solutions.

Original language	English
Pages (from-to)	26-32
Number of pages	7
Journal	Experimental Mathematics
Volume	32
Issue number	1
DOIs	https://doi.org/10.1080/10586458.2020.1753597
State	Published - 2023

Keywords

CPn
Energy minimization
equiangular tight frame
frame potential

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10.1080/10586458.2020.1753597

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abstract = "In this paper we discuss minimizing a generalized frame potential - F(p,m,n) - for vectors in CPn. We discuss the minimal frame potential as well as the space of solutions for the minimization problem. We investigate this question both numerically and analytically. We find that for some values of p - Equiangular Tight Frames (ETF) are unique solutions, in contrast to the case of p = 2 where they are non-unique solutions.",

keywords = "CPn, Energy minimization, equiangular tight frame, frame potential",

author = "{Ben Av}, Radel and Giora Dula and Assaf Goldberger and Yossi Strassler",

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year = "2023",

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AU - Goldberger, Assaf

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Y1 - 2023

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AB - In this paper we discuss minimizing a generalized frame potential - F(p,m,n) - for vectors in CPn. We discuss the minimal frame potential as well as the space of solutions for the minimization problem. We investigate this question both numerically and analytically. We find that for some values of p - Equiangular Tight Frames (ETF) are unique solutions, in contrast to the case of p = 2 where they are non-unique solutions.

KW - CPn

KW - Energy minimization

KW - equiangular tight frame

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Frame Potential in CPⁿ Some Numerical and Analytical Results

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Keywords

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