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Orthogonal polynomial projection error in Dunkl–Sobolev norms in the ball
Journal of Approximation Theory ( IF 0.9 ) Pub Date : 2020-10-15 , DOI: 10.1016/j.jat.2020.105495 Gonzalo A. Benavides , Leonardo E. Figueroa
中文翻译:
球的Dunkl–Sobolev范数中的正交多项式投影误差
更新日期:2020-11-02
Journal of Approximation Theory ( IF 0.9 ) Pub Date : 2020-10-15 , DOI: 10.1016/j.jat.2020.105495 Gonzalo A. Benavides , Leonardo E. Figueroa
We study approximation properties of weighted -orthogonal projectors onto spaces of polynomials of bounded degree in the Euclidean unit ball, where the weight is of the reflection-invariant form , . Said properties are measured in Dunkl–Sobolev-type norms in which the same weighted norm is used to control all the involved differential–difference Dunkl operators, such as those appearing in the Sturm–Liouville characterization of similarly weighted -orthogonal polynomials, as opposed to the partial derivatives of Sobolev-type norms.
中文翻译:
球的Dunkl–Sobolev范数中的正交多项式投影误差
我们研究加权的近似性质 正交投影仪投影到欧几里得单位球中有界度多项式的空间,其中权重为不变反射形式 , 。所述属性以Dunkl-Sobolev型规范衡量,其中相同的权重 范数用于控制所有涉及的微分-差分Dunkl算子,例如在Sturm-Liouville表征相似加权的算子中出现的算子 -正交多项式,与Sobolev型规范的偏导数相反。