论文标题
dunkl-sobolev规范中的正交多项式投影误差
Orthogonal polynomial projection error in Dunkl-Sobolev norms in the ball
论文作者
论文摘要
我们将加权$ \ mathrm {l}^2 $ - 正交投影仪的近似特性研究到欧几里得单元球中有界程度的多项式的空间，其中重量是反射不变的形式$（1- \ lvert x \ rvert x \ rvert x \ rvert x \ rvert^2） \ rvert^{γ_i} $，$α，γ_1，\ dots，γ_d> -1 $。所述物业以Dunkl-Sobolev型规范来衡量，其中相同的加权$ \ Mathrm {l}^2 $ norm用于控制所有所涉及的差异差异dunkl操作员，例如那些出现在sturm-liouville表征相似加权$ \ mathrm a andiriv to poptiriv pocky poptiriv to to pockert offoct的dunkl octiant offormial offyers and offiriv to to to possight an Sobolev型规范。证明的方法依赖于空间而不是正交多项式的基础，这极大地简化了博览会。
We study approximation properties of weighted $\mathrm{L}^2$-orthogonal projectors onto spaces of polynomials of bounded degree in the Euclidean unit ball, where the weight is of the reflection-invariant form $(1-\lVert x \rVert^2)^α\prod_{i=1}^d \lvert x_i \rvert^{γ_i}$, $α, γ_1, \dots, γ_d > -1$. Said properties are measured in Dunkl-Sobolev-type norms in which the same weighted $\mathrm{L}^2$ norm is used to control all the involved differential-difference Dunkl operators, such as those appearing in the Sturm-Liouville characterization of similarly weighted $\mathrm{L}^2$-orthogonal polynomials, as opposed to the partial derivatives of Sobolev-type norms. The method of proof relies on spaces instead of bases of orthogonal polynomials, which greatly simplifies the exposition.
