Localizable operators and the construction of localized frames
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- by Fumiko Futamura
- Proc. Amer. Math. Soc. 137 (2009), 4187-4197
- DOI: https://doi.org/10.1090/S0002-9939-09-09995-X
- Published electronically: July 14, 2009
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Abstract:
We introduce the notion of localizable operators with respect to frames and prove the boundedness of such operators on families of Banach spaces. This generalizes previous results for specific operators, such as pseudodifferential operators on modulation spaces. We also use this notion to provide sufficient conditions for the construction of frames which have the localization property.References
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Bibliographic Information
- Fumiko Futamura
- Affiliation: Department of Mathematics and Computer Science, Southwestern University, Georgetown, Texas 78626
- Email: futamurf@southwestern.edu
- Received by editor(s): January 22, 2009
- Received by editor(s) in revised form: April 5, 2009
- Published electronically: July 14, 2009
- Communicated by: Michael T. Lacey
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 4187-4197
- MSC (2000): Primary 42C15, 46B15, 47B37, 47L80
- DOI: https://doi.org/10.1090/S0002-9939-09-09995-X
- MathSciNet review: 2538579