Localizable operators and the construction of localized frames

Futamura, Fumiko

doi:10.1090/S0002-9939-09-09995-X

Localizable operators and the construction of localized frames
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Proc. Amer. Math. Soc. 137 (2009), 4187-4197 Request permission

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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