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Nonlinear approximation of harmonic functions from shifts of the Newtonian kernel in BMO
Kamen G. Ivanov, Pencho Petrushev
We study nonlinear n-term approximation of harmonic functions on the unit ball in from linear combinations of shifts of the Newtonian kernel (fundamental solution of the Lapl…
Nonlinear spline approximation in
Kamen G. Ivanov, Pencho Petrushev
We study nonlinear approximation in from splines generated by a hierarchy of B-splines over regular multilevel nested partitions of . Companion Jack…
Nonlinear -term approximation of harmonic functions from shifts of the Newtonian Kernel
Kamen Ivanov, Pencho Petrushev
A basic building block in Classical Potential Theory is the fundamental solution of the Laplace equation in (Newtonian kernel). The main goal of this article is to…
Highly localized kernels on the sphere induced by Newtonian kernels
Kamen Ivanov, Pencho Petrushev
The purpose of this article is to construct highly localized summability kernels on the unit sphere in that are restrictions to the sphere of linear combinations of…
Decomposition of spaces of distributions induced by tensor product bases
Kamen Ivanov, Pencho Petrushev, Yuan Xu
Rapidly decaying kernels and frames (needlets) in the context of tensor product Jacobi polynomials are developed based on several constructions of multivariate cutoff fu…
Sub-exponentially localized kernels and frames induced by orthogonal expansions
Kamen Ivanov, Pencho Petrushev, Yuan Xu
The aim of this paper is to construct sup-exponentially localized kernels and frames in the context of classical orthogonal expansions, namely, expansions in Jacobi polynomials, sp…