Disk polynomials form a basis of orthogonal polynomials on the disk corresponding to the radial weight \({\alpha +1 \over \pi }(1-r^{2})^{\alpha }\). 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.

中文翻译：

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磁盘多项式的稳定性

磁盘多项式在磁盘上形成正交多项式的基础，该多项式与径向权重\（{\ alpha +1 \ over \ pi}（1-r ^ {2}）^ {\ alpha} \相对应。本文分析了磁盘多项式的稳定性。引入并限制了与此最小二乘近似表示相关的条件。在所有圆盘多项式中，获得与α = 0相对应的Zernike多项式的最小边界。