Vol. 11, No. 3, 2018

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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
Abstract

This paper extends three results from classical finite frame theory over real or complex numbers to binary frames for the vector space 2d. 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