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

 

Orthonormal dilations of non-tight frames


Authors: Marcin Bownik, John Jasper and Darrin Speegle
Journal: Proc. Amer. Math. Soc. 139 (2011), 3247-3256
MSC (2010): Primary 42C15, 47B15; Secondary 46C05
Published electronically: February 11, 2011
MathSciNet review: 2811280
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Abstract: We establish dilation theorems for non-tight frames with additional structure, i.e., frames generated by unitary groups of operators and projective unitary representations. This generalizes previous dilation results for Parseval frames due to Han and Larson, and Gabardo and Han. We also extend the dilation theorem for Parseval wavelets due to Dutkay, Han, Picioroaga, and Sun by identifying the optimal class of frame wavelets for which dilation into an orthonormal wavelet is possible.


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Additional Information

Marcin Bownik
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403–1222
Email: mbownik@uoregon.edu

John Jasper
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403–1222
Email: jjasper@uoregon.edu

Darrin Speegle
Affiliation: Department of Mathematics and Computer Science, Saint Louis University, 221 N. Grand Boulevard, St. Louis, Missouri 63103
Email: speegled@slu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10887-6
PII: S 0002-9939(2011)10887-6
Keywords: Frame, orthonormal dilation, projective unitary representation, Gabor system, Baumslag-Solitar group, wavelet
Received by editor(s): August 5, 2010
Published electronically: February 11, 2011
Additional Notes: The first and second authors were partially supported by NSF grant DMS-0653881.
Communicated by: Richard Rochberg
Article copyright: © Copyright 2011 American Mathematical Society