基于BMO中牛顿核位移的调和函数的非线性逼近

IF 0.6 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2026-03-01 Epub Date: 2025-10-10 DOI:10.1016/j.jat.2025.106246

Kamen G. Ivanov , Pencho Petrushev

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引用次数: 0

摘要

从BMO中牛顿核位移的线性组合（拉普拉斯方程的基本解）出发，研究了Rd中单位球上调和函数的非线性n项逼近。建立了一个Jackson估计，该估计自然涉及BMO的Sobolev嵌入线上的Besov空间。得到这一结果的方法是基于构造Besov空间和球上的VMO的高度局域框架，这些框架的元素是牛顿核位移的固定次数的线性组合。

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Nonlinear approximation of harmonic functions from shifts of the Newtonian kernel in BMO

We study nonlinear

n

-term approximation of harmonic functions on the unit ball in

R^{d}

from linear combinations of shifts of the Newtonian kernel (fundamental solution of the Laplace equation) in BMO. A Jackson estimate is established that naturally involves Besov spaces lying on the Sobolev embedding line for BMO. The method for obtaining this result is based on the construction of highly localized frames for Besov spaces and VMO on the sphere whose elements are linear combinations of a fixed number of shifts of the Newtonian kernel.

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来源期刊

Journal of Approximation Theory 数学-数学

CiteScore

1.90

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others: • Classical approximation • Abstract approximation • Constructive approximation • Degree of approximation • Fourier expansions • Interpolation of operators • General orthogonal systems • Interpolation and quadratures • Multivariate approximation • Orthogonal polynomials • Padé approximation • Rational approximation • Spline functions of one and several variables • Approximation by radial basis functions in Euclidean spaces, on spheres, and on more general manifolds • Special functions with strong connections to classical harmonic analysis, orthogonal polynomial, and approximation theory (as opposed to combinatorics, number theory, representation theory, generating functions, formal theory, and so forth) • Approximation theoretic aspects of real or complex function theory, function theory, difference or differential equations, function spaces, or harmonic analysis • Wavelet Theory and its applications in signal and image processing, and in differential equations with special emphasis on connections between wavelet theory and elements of approximation theory (such as approximation orders, Besov and Sobolev spaces, and so forth) • Gabor (Weyl-Heisenberg) expansions and sampling theory.