Equiangular frames and generalizations of the Welch bound to dual pairs of frames

Ole Christensen, Somantika Datta, Rae Young Kim*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

The purpose of this paper is twofold. First, we determine the lower bound for the maximum coherence between a pair of dual frames in and state conditions under which the lower bound is attained. It is shown that the existence of frames and duals that attain the lower bound is related to the existence of equiangular tight frames (ETFs). Second, motivated by the scarcity of ETFs (which by default have dual ETFs), we examine the more general question of existence of equiangular frames that have equiangular duals. For the case where an equiangular dual cannot be found we provide conditions under which the number of angles among vectors in the canonical dual frame is small.
Original languageEnglish
JournalLinear and Multilinear Algebra
Pages (from-to)1-11
ISSN1563-5139
DOIs
Publication statusPublished - 2019

Keywords

  • Dual frames
  • Equiangular frames
  • Tight frames
  • Welch bound

Cite this

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title = "Equiangular frames and generalizations of the Welch bound to dual pairs of frames",
abstract = "The purpose of this paper is twofold. First, we determine the lower bound for the maximum coherence between a pair of dual frames in and state conditions under which the lower bound is attained. It is shown that the existence of frames and duals that attain the lower bound is related to the existence of equiangular tight frames (ETFs). Second, motivated by the scarcity of ETFs (which by default have dual ETFs), we examine the more general question of existence of equiangular frames that have equiangular duals. For the case where an equiangular dual cannot be found we provide conditions under which the number of angles among vectors in the canonical dual frame is small.",
keywords = "Dual frames, Equiangular frames, Tight frames, Welch bound",
author = "Ole Christensen and Somantika Datta and Kim, {Rae Young}",
year = "2019",
doi = "10.1080/03081087.2019.1586825",
language = "English",
pages = "1--11",
journal = "Linear and Multilinear Algebra",
issn = "1563-5139",
publisher = "Taylor and Francis Ltd.",

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Equiangular frames and generalizations of the Welch bound to dual pairs of frames. / Christensen, Ole; Datta, Somantika; Kim, Rae Young.

In: Linear and Multilinear Algebra, 2019, p. 1-11.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Equiangular frames and generalizations of the Welch bound to dual pairs of frames

AU - Christensen, Ole

AU - Datta, Somantika

AU - Kim, Rae Young

PY - 2019

Y1 - 2019

N2 - The purpose of this paper is twofold. First, we determine the lower bound for the maximum coherence between a pair of dual frames in and state conditions under which the lower bound is attained. It is shown that the existence of frames and duals that attain the lower bound is related to the existence of equiangular tight frames (ETFs). Second, motivated by the scarcity of ETFs (which by default have dual ETFs), we examine the more general question of existence of equiangular frames that have equiangular duals. For the case where an equiangular dual cannot be found we provide conditions under which the number of angles among vectors in the canonical dual frame is small.

AB - The purpose of this paper is twofold. First, we determine the lower bound for the maximum coherence between a pair of dual frames in and state conditions under which the lower bound is attained. It is shown that the existence of frames and duals that attain the lower bound is related to the existence of equiangular tight frames (ETFs). Second, motivated by the scarcity of ETFs (which by default have dual ETFs), we examine the more general question of existence of equiangular frames that have equiangular duals. For the case where an equiangular dual cannot be found we provide conditions under which the number of angles among vectors in the canonical dual frame is small.

KW - Dual frames

KW - Equiangular frames

KW - Tight frames

KW - Welch bound

U2 - 10.1080/03081087.2019.1586825

DO - 10.1080/03081087.2019.1586825

M3 - Journal article

SP - 1

EP - 11

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 1563-5139

ER -