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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A new identity for Parseval frames


Authors: Radu Balan, Peter G. Casazza, Dan Edidin and Gitta Kutyniok
Journal: Proc. Amer. Math. Soc. 135 (2007), 1007-1015
MSC (2000): Primary 42C15; Secondary 94A12
Published electronically: November 14, 2006
MathSciNet review: 2262901
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Abstract: In this paper we establish a surprising new identity for Parseval frames in a Hilbert space. Several variations of this result are given, including an extension to general frames. Finally, we discuss the derived results.


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Additional Information

Radu Balan
Affiliation: Siemens Corporate Research, 755 College Road East, Princeton, New Jersey 08540
Email: radu.balan@siemens.com

Peter G. Casazza
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: pete@math.missouri.edu

Dan Edidin
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: edidin@math.missouri.edu

Gitta Kutyniok
Affiliation: Institute of Mathematics, Justus-Liebig-University Giessen, 35392 Giessen, Germany
Email: gitta.kutyniok@math.uni-giessen.de

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08930-1
PII: S 0002-9939(06)08930-1
Keywords: Bessel sequence, frame, Hilbert space, Parseval frame, Parseval Frame Identity
Received by editor(s): June 13, 2005
Published electronically: November 14, 2006
Additional Notes: The second author was supported by NSF DMS 0405376.
The third author was supported by NSA MDA 904-03-1-0040.
The fourth author was supported by DFG research fellowship KU 1446/5.
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2006 American Mathematical Society