Vol. 9, No. 2, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 11, 1 issue

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
Cover Page
Editorial Board
Editors’ Addresses
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Subscriptions
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Factor posets of frames and dual frames in finite dimensions

Kileen Berry, Martin S. Copenhaver, Eric Evert, Yeon Hyang Kim, Troy Klingler, Sivaram K. Narayan and Son T. Nghiem

Vol. 9 (2016), No. 2, 237–248
Abstract

We consider frames in a finite-dimensional Hilbert space, where frames are exactly the spanning sets of the vector space. A factor poset of a frame is defined to be a collection of subsets of I, the index set of our vectors, ordered by inclusion so that nonempty J I is in the factor poset if and only if {fi}iJ is a tight frame. We first study when a poset P 2I is a factor poset of a frame and then relate the two topics by discussing the connections between the factor posets of frames and their duals. Additionally we discuss duals with regard to p-minimization.

Keywords
frames, tight frames, factor poset, $\ell_p$-norm
Mathematical Subject Classification 2010
Primary: 42C15, 05B20, 15A03
Milestones
Received: 26 September 2014
Revised: 28 February 2015
Accepted: 27 March 2015
Published: 2 March 2016

Communicated by David Royal Larson
Authors
Kileen Berry
Department of Mathematics
University of Tennessee
Knoxville, TN 37996
United States
Martin S. Copenhaver
Operations Research Center
Massachusetts Institute of Technology
Cambridge, MA 02139
United States
Eric Evert
Department of Mathematics
University of California, San Diego
La Jolla, CA 92093
United States
Yeon Hyang Kim
Department of Mathematics
Central Michigan University
Mount Pleasant, MI 48859
United States
Troy Klingler
Department of Mathematics
Central Michigan University
Mount Pleasant, MI 48859
United States
Sivaram K. Narayan
Department of Mathematics
Central Michigan University
Mount Pleasant, MI 48859
United States
Son T. Nghiem
Berea College
Berea, KY 40403
United States