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Localizable operators and the construction of localized frames
Author(s):
Fumiko
Futamura
Journal:
Proc. Amer. Math. Soc.
137
(2009),
4187-4197.
MSC (2000):
Primary 42C15, 46B15, 47B37, 47L80
Posted:
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:
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
Posted:
July 14, 2009
Communicated by:
Michael T. Lacey
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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