Orthonormal dilations of non-tight frames
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- by Marcin Bownik, John Jasper and Darrin Speegle PDF
- Proc. Amer. Math. Soc. 139 (2011), 3247-3256 Request permission
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.References
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Additional Information
- Marcin Bownik
- Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403–1222
- MR Author ID: 629092
- Email: mbownik@uoregon.edu
- John Jasper
- Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403–1222
- MR Author ID: 937075
- 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
- 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
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 139 (2011), 3247-3256
- MSC (2010): Primary 42C15, 47B15; Secondary 46C05
- DOI: https://doi.org/10.1090/S0002-9939-2011-10887-6
- MathSciNet review: 2811280