Approximation by multivariate quasi-projection operators and Fourier multipliers

作者：

Highlights：

• The study of wide classes of multivariate quasi-projection operators.

• New upper and lower estimates of the approximation error.

• The results are given in terms of Fourier multipliers.

• Estimates in terms of anisotropic moduli of smoothness and best approximations.

• New general Whittaker–Nyquist–Kotelnikov–Shannon-type theorems.

摘要

•The study of wide classes of multivariate quasi-projection operators.•New upper and lower estimates of the approximation error.•The results are given in terms of Fourier multipliers.•Estimates in terms of anisotropic moduli of smoothness and best approximations.•New general Whittaker–Nyquist–Kotelnikov–Shannon-type theorems.

论文关键词：Quasi-projection operator,Besov space,Error estimate,Anisotropic best approximation,Anisotropic moduli of smoothness,Fourier multipliers

论文评审过程：Received 5 July 2020, Revised 25 December 2020, Accepted 3 January 2021, Available online 26 February 2021, Version of Record 26 February 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.125955