The Mathematical Theory of Wavelets

By Guido L. Weiss, E. Wilson. 2001

86 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Geophysics

View Paper: https://www.semanticscholar.org/paper/924d3ff3167ba7a6680b2109140d74d1472be9e5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Demetrio Labate
2. Wang-Q Lim
3. Zuowei Shen
4. Kanghui Guo
5. Hartmut Fuhr
6. Guido L. Weiss
7. Amos Ron
8. E. Wilson

In Computer Vision and Pattern Recognition

1. Demetrio Labate
2. Wang-Q Lim
3. Zuowei Shen
4. Kanghui Guo
5. Amos Ron
6. Guido L. Weiss
7. Hartmut Fuhr
8. E. Wilson

In Geophysics

1. Wang-Q Lim
2. Demetrio Labate
3. Hartmut Fuhr
4. Kanghui Guo
5. Guido L. Weiss
6. E. Wilson
7. Zuowei Shen
8. Gitta Kutyniok

Citations in the corpus

• Generalized Shift-Invariant Systems (2005, background): “The above conjecture was proved true before for an integer dilation matrix: in [ WW ] for the dyadic dilation system (i.e., s = 2 Id), and in [Bo] and in [R] for a general integer expansive matrix s.”
• The Theory of Wavelets with Composite Dilations (2006, result): “Observe that this result generalizes the corresponding result for the classical MRA, where the number of generators needed to obtain an orthonormal MRA A-wavelet is given by L = | det a|−1 (cf., for example, [ 18 ]).”
• The Spectral Function of Shift-Invariant Spaces (2003, background): “Although [BDR1] and Helson’s range function [He1] is the origin of this approach, it is thanks to Weiss (see [WW]) that the spectral function has a very elementary definition.”
• The structure of shift invariant spaces on a locally compact abelian group (2008, background): “3, we have the following corollary (see also [16]).”
• A unified characterization of reproducing systems generated by a finite family, II (2002, background): “For example, it was recently pointed out by Weiss and Wilson [ 30 ], that the translations, more than the dilations, play a critical role in the discretization of continuous wavelets.”
• Abstract Harmonic Analysis of Continuous Wavelet Transforms (2005, background): “• The characterization of dilation groups allowing the existence of admissible vectors was addressed in full generality in [77, 113], as well as in [52], and the discussion in the first two sections follows the latter paper closely.”