Localized Polynomial Frames on the Ball
By Pencho Petrushev, Yuan Xu. 2006
80 citations recorded by the source corpus.
Almost exponentially localized polynomial kernels are constructed on the unit ball $B^d$ in $\mbox{\bf R}^d$ with weights $w_\mu(x)= (1-|x|^2)^{\mu-1/2}, \mu \ge 0$, by smoothing out the coefficients of the corresponding orthogonal projectors. These kernels are utilized to the design of cubature formulas on $B^d$ with respect to $w_\mu(x)$ and to the construction of polynomial tight frames in $L^2(B^d, w_\mu)$ (called needlets) whose elements have nearly exponential localization.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/83b600f831588134b1e5850b7f4c2a3b83f072e8
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In Applied Mathematics
- Gerard Kerkyacharian
- T. Coulhon
- Pencho Petrushev
- Yuan Xu
- Feng Dai
- Dominique Picard
- P. Auscher
- Daryl Geller
Citations in the corpus
- Decomposition of Spaces of Distributions Induced by Hermite Expansions (2007, methodology): “Our development here is a part of a bigger project for needlet characterization of Triebel-Lizorkin and Besov spaces on nonclassical domains such as the unit sphere [11], the interval with Jacobi weights [8, 13], and the unit ball [9, 14].”
- Heat Kernel Generated Frames in the Setting of Dirichlet Spaces (2012, methodology): “the development of frames and weighted Besov and Triebel-Lizorkin spaces on the unit ball B in R in [36, 48], which perfectly fit in our general setting, but we shall not pursue in this article.”