Abstract
Several concepts for the localization of a frame are studied. The intrinsic localization of a frame is defined by the decay properties of its Gramian matrix. Our main result asserts that the canonical dual frame possesses the same intrinsic localization as the original frame. The proof relies heavily on Banach algebra techniques, in particular on recent spectral invariance properties for certain Banach algebras of infinite matrices. Intrinsically localized frames extend in a natural way to Banach frames for a class of associated Banach spaces which are defined by weighted ℓp-coefficients of their frame expansions. As an example, the time--frequency concentration of distributions is characterized by means of localized (nonuniform) Gabor frames.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Fornasier, M., Gröchenig, . Intrinsic Localization of Frames. Constr Approx 22, 395–415 (2005). https://doi.org/10.1007/s00365-004-0592-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00365-004-0592-3