Localization of frames II

By Elena Cordero, Karlheinz Gröchenig. 2004

50 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/d3def6ebf89793784b99bbf2a6f439efeec02c8c

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In Applied Mathematics

In Computer Vision and Pattern Recognition

Citations in the corpus

Stability of Localized Operators (2008, methodology): “For example, the classical Wiener’s lemma and its weighted variation ([39]) were used to establish the decay property at infinity for dual generators of a shift-invariant space ([1,43]); the Wiener’s lemma for matrices associated with twisted convolution was used in the study the decay properties of”
Modulation Spaces: Looking Back and Ahead (2006, unknown): “[33] E.”
Symmetry and inverse-closedness of matrix algebras and functional calculus for infinite matrices (2006, background): “The concept of localization makes frame expansions meaningful for other Banach spaces besides 77 [19] and plays a key role in the characterization of certain Banach spaces by means of frames and in the investigations of sparse representations with frames [19, 10].”
Wiener’s Lemma for Infinite Matrices II (2007, methodology): “... decay property at infinity for dual generators of a shift-invariant space ([1, 27]); the Wiener’s lemma for matrices associated with twisted convolution was used in the study the decay properties of the dual Gabor frame for L2 ([3, 23, 24]); the Jaard’s result ([26]) for infinite matrices with p”
Banach frames for α-modulation spaces (2007, background): “New tools for extending an L2-frame to Banach frames and atomic decompositions have been introduced by Gröchenig.”
Wiener's lemma for infinite matrices with polynomial off-diagonal decay (2005, methodology): “frequency analysis [2,10–13,19], shift-invariant spaces and polynomial spline spaces [1,8,15,19], and non sampling [6,19].”
Intrinsic Localization of Frames (2005, methodology): “For (b) we use the inequalities C −1 m(k) ≤ m(k +u) ≤ Cm(k) for all u ∈ [0, 1 ] d because m is assumed to be v-moderate.”