Non-radial weights and polynomial approximation in spaces of analytic functions

TL;DR

This paper investigates conditions on various weight functions, including radial and non-radial types, that enable approximation of functions in certain analytic spaces using polynomials.

Contribution

It extends polynomial approximation theory to include non-radial and angular weights, broadening the class of weights for which approximation is feasible.

Findings

Established sufficient conditions for polynomial approximation with non-radial weights

Included angular weights in the approximation framework

Expanded the understanding of weighted spaces of analytic functions

Abstract

We study sufficient conditions on weight functions under which norm approximations by analytic polynomials are possible. The weights we study include radial, non-radial, and angular weights.