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Kamen G. Ivanov

Publications and source records attributed to Kamen G. Ivanov.

2 recordsLinked to original sources
arXiv2025

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 sharp Jackson estimate is established that naturally involves certain Besov spaces. 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.

math.CA↗
arXiv2020

Nonlinear spline approximation in $\operatorname{BMO}(\mathbb R)$

We study nonlinear approximation in $\operatorname{BMO}$ from splines generated by a hierarchy of B-splines over regular multilevel nested partitions of $\mathbb R$. Companion Jackson and Bernstein estimates are established that allow to completely characterize the associated approximation spaces.

math.CA↗