A unified characterization of reproducing systems generated by a finite family, II

By Eugenio Hernández, Demetrio Labate, Guido L. Weiss. 2002

154 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c9628ab630e7c78060bd71201851b78a3b4e5b78

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Mathematical Physics

Citations in the corpus

Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2(Rd) (2004, unknown): “For the case of regular lattices Guido Weiss and his group [HDW02, HDW03, Lab02 ] developed a very fundamental program to characterize a large class of decompositions of L2(Rd) through certain equations that the generators must satisfy.”
Wavelets with composite dilations and their MRA properties (2006, background): “1 in [13] gives the following complete characterization of all functions Ψ = {ψ1, .”
History and Evolution of the Density Theorem for Gabor Frames (2007, background): “In [139] it is shown that the local integrability condition of [114] is equivalent to finite affine Beurling density (assuming some mild regularity on the wavelet ψ).”
Banach frames for α-modulation spaces (2007, background): “[38,39] and Labate [44] developed characterizations of a large class of mixed decompositions in L2 as an attempt of a unified approach to Gabor, wavelet and more general wave packet frames.”
Riesz and frame systems generated by unitary actions of discrete groups (2014, background): “They have been the main subject of an increasing number of works in the last twenty five years due to their role in approximation theory [31, 33, 14, 15, 36, 4, 3, 5, 23, 37, 24, 7, 2].”
Linear Independence of Finite Gabor Systems (2006, methodology): “e. There are useful recent characterizations of frames that apply in both the wavelet and Gabor settings by Hern´ andez, Labate, and Weiss [90], [ 73 ].”
Reproducing formulas for generalized translation invariant systems on locally compact abelian groups (2014, methodology): “The main result of Hernández, Labate, and Weiss [30] is a characterization, by so-called tα-equations, of all functions gj that give rise to isometric, isomorphic transforms, called Parseval frames in frame theory.”
Generalized Shift-Invariant Systems (2005, methodology): “One should consider our effort here and that of [28] as “concurrent and independent.”
Generalized Shift-Invariant Systems and Frames for Subspaces (2005, methodology): “Characterizations of dual frame pairs in this setting have been obtained by Hernandez, Labate, and Weiss [11] as well as by Ron and Shen [16].”
The Theory of Wavelets with Composite Dilations (2006, background): “In [ 14 ], however, one finds examples of admissible dilation sets A = {a i : i ∈ Z}, where the matrix a ∈ GLn(R) is not expanding.”
Oversampling, quasi-affine frames, and wave packets (2004, background): “[4], [20], [17], [19], [15]).”