Stability properties of disk polynomials

Disk polynomials form a basis of orthogonal polynomials on the disk corresponding to the radial weight α+1π(1−r2)α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\alpha +1 \over \pi }(1-r^{2})^{\alpha }$\end{document}. In this paper, the stability properties of disk polynomials are analyzed. A conditioning associated with the representation of the least squares approximation with respect to this basis is introduced and bounded. Among all disk polynomials, the least bounds are obtained for Zernike polynomials corresponding to α = 0.