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

 

Localizable operators and the construction of localized frames


Author: Fumiko Futamura
Journal: Proc. Amer. Math. Soc. 137 (2009), 4187-4197
MSC (2000): Primary 42C15, 46B15, 47B37, 47L80
Published electronically: July 14, 2009
MathSciNet review: 2538579
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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.


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Additional Information

Fumiko Futamura
Affiliation: Department of Mathematics and Computer Science, Southwestern University, Georgetown, Texas 78626
Email: futamurf@southwestern.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09995-X
PII: S 0002-9939(09)09995-X
Keywords: Localized frames, localizable operators, Banach frames
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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.