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

 

Equivalence relations and distances
between Hilbert frames


Author: Radu Balan
Journal: Proc. Amer. Math. Soc. 127 (1999), 2353-2366
MSC (1991): Primary 42C99, 46C99
Published electronically: April 8, 1999
MathSciNet review: 1600096
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Abstract | References | Similar Articles | Additional Information

Abstract: We study some equivalency relations between Hilbert frames and closed subspaces of $l^2(\mathbf{I})$. We define also a distance between frames and we establish the geometric meaning of this metric. Finally we find the closest and respectively the nearest tight frame to a given frame.


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Additional Information

Radu Balan
Affiliation: Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544
Email: rvbalan@math.princeton.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04826-1
PII: S 0002-9939(99)04826-1
Keywords: Closeness bound, nearness, quadratic distance between frames
Received by editor(s): October 31, 1997
Published electronically: April 8, 1999
Additional Notes: The author is grateful to Ingrid Daubechies for the many hours of working together and for the continuous support and encouragement. He also thanks David Larson for a copy of his paper.
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society