Approximation properties of multivariate quasi-projection operators are studied. Wide classes of such operators are considered, including the sampling and the Kantorovich-Kotelnikov type operators generated by different band-limited functions. The rate of convergence in the weighted $L_p$-spaces for these operators is investigated. The results allow us to estimate the error for reconstruction of signals (approximated functions) whose decay is not enough to be in $L_p$.

中文翻译：

---

加权L _p空间中的拟投影算子

研究了多元拟投影算子的逼近性质。考虑了这类运算符的大类，包括由不同的带限函数生成的采样运算符和Kantorovich-Kotelnikov型运算符。加权的收敛速度${\mathrm{大号}}_p$研究这些运算符的空间。结果使我们能够估计信号衰减（近似函数）的误差，其衰减不足以使${\mathrm{大号}}_p$。