单位球面上函数的加权逼近
Weighted Approximation of functions on the unit sphere
摘要：
建立了$\RR^{d+1}$单位球面上加权$L^p$空间中最佳逼近的正逆定理，其中权函数权函数在有限反射群下是不变的.定理是使用高阶光滑模，这被证明是等价的$K$ -功能定义使用的权力的球形$h$ -拉普拉斯算子。此外，对于单位球上的加权逼近和$\RR^d$的单形上的加权逼近也得到了类似的结果。
英文摘要：
The direct and inverse theorems are established for the best approximation in the weighted $L^p$ space on the unit sphere of $\RR^{d+1}$, in which the weight functions are invariant under finite reflection groups. The theorems are stated using a modulus of smoothness of higher order, which is proved to be equivalent to a $K$-functional defined using the power of the spherical $h$-Laplacian. Furthermore, similar results are also established for weighted approximation on the unit ball and on the simplex of $\RR^d$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
