Open AccessLocalizable operators and the construction of localized frames
Author(s) -
Fumiko Futamura
Publication year - 2009
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-09-09995-x
Subject(s) - pseudodifferential operators , mathematics , property (philosophy) , operator theory , banach space , pure mathematics , frame (networking) , algebra over a field , discrete mathematics , computer science , telecommunications , epistemology , philosophy
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.