Localized polynomial frames on the ball

2006/11/06 by Pencho Petrushev, Yuan Xu, Petrushev, Pencho +1 · 3 citations
Mathematics · #42B35 #42C40 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.math/0611145

openalex publication_date 2006/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Almost exponentially localized polynomial kernels are constructed on the unit ball B^d in \RR^d with weights %functions W_μ(x)= (1-|x|²)^μ-1/2, μ≥ 0, by smoothing out the coefficients of the corresponding orthogonal projectors. These kernels are utilized to the design of cubature formulae on B^d with respect to W_μ(x) and to the construction of polynomial tight frames in L²(B^d, W_μ) (called needlets) whose elements have nearly exponential localization.

Citations

• The spectral function of an elliptic operator

Cited by

• On Dirichlet Spaces of Homogeneous Type Via Heat Kernel
• On Bernstein inequalities on the unit ball
• Approximation and orthogonality on fully symmetric domains

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