Nonlinear $n$-term approximation of harmonic functions from shifts of the Newtonian kernel

DOI10.1090/tran/8071zbMath1440.42108arXiv1808.08641OpenAlexW2998966715MaRDI QIDQ4960230

Kamen G. Ivanov, Pencho P. Petrushev

Publication date: 9 April 2020

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.08641

zbMATH Keywords

Hardy spacesBesov spacesharmonic functionsnonlinear approximationNewtonian kernelframe decomposition

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) General harmonic expansions, frames (42C15) Rate of convergence, degree of approximation (41A25)

Related Items (1)

Highly localized summability kernels on the sphere induced by Newtonian kernels

Uses Software

• DLMF

Cites Work

• Harmonic Besov and Triebel-Lizorkin spaces on the ball
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• vector-valued singular integrals and maximal functions on spaces of homogeneous type
• Some observations on Besov and Lizorkin-Triebel spaces.
• Approximation Theory and Harmonic Analysis on Spheres and Balls
• Rational bases for spaces of holomorphic functions in the disc
• Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces
• Spherical Harmonics
• Potential theory
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