论文标题
按周期性多元准投影算子进行近似
Approximation by periodic multivariate quasi-projection operators
论文作者
论文摘要
研究了具有基质扩张的周期性准投影算子的近似特性。此类操作员由一系列函数$φ_j$和一系列分布/函数$ \widetildeφ_j$生成。采样型准投影操作员的错误估计值是在$φ_j$的定期stramp-fix条件下获得的，以及$φ_j$和$ \wideTildeLdeφ_j$的兼容性条件。这些估计是根据近似功能的傅立叶系数给出的，并提供了一些已知的非周期性结果的类似物。在一些其他假设下，误差估计是在其他术语中给出的，特别是使用最佳近似值。提供了许多示例。
Approximation properties of periodic quasi-projection operators with matrix dilations are studied. Such operators are generated by a sequence of functions $φ_j$ and a sequence of distributions/functions $\widetildeφ_j$. Error estimates for sampling-type quasi-projection operators are obtained under the periodic Strang-Fix conditions for $φ_j$ and the compatibility conditions for $φ_j$ and $\widetildeφ_j$. These estimates are given in terms of the Fourier coefficients of approximated functions and provide analogs of some known non-periodic results. Under some additional assumptions error estimates are given in other terms in particular using the best approximation. A number of examples are provided.
