Binary frames with prescribed dot products and frame operator

Furst, Veronika; Smith, Eric P.

doi:10.2140/involve.2018.11.519

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Binary frames with prescribed dot products and frame operator

Veronika Furst and Eric P. Smith

Vol. 11 (2018), No. 3, 519–540

DOI: 10.2140/involve.2018.11.519

Abstract

This paper extends three results from classical finite frame theory over real or complex numbers to binary frames for the vector space $ℤ_{2}^{d}$ . Without the notion of inner products or order, we provide an analog of the “fundamental inequality” of tight frames. In addition, we prove the binary analog of the characterization of dual frames with given inner products and of general frames with prescribed norms and frame operator.

Keywords

frames, binary vector spaces, frame operators, Gramian matrices

Mathematical Subject Classification 2010

Primary: 15A03, 15A23, 15B33, 42C15

Milestones

Received: 24 May 2017

Accepted: 17 July 2017

Published: 20 October 2017

Communicated by David Royal Larson

Authors

Veronika Furst
Department of Mathematics Fort Lewis College Durango, CO United States

Eric P. Smith
Department of Mathematics Fort Lewis College Durango, CO United States

Vol. 11, No. 3, 2018