Asymptotics of the Lebesgue constants for bivariate approximation processes

作者：

Highlights：

• Asymptotics of the Lebesgue constant for the Lagrange interpolation based on the Lissajous-Chebyshev node points.

• Asymptotics of the Lebesgue constant for the partial sums of the Fourier series generated by the anisotropically dilated rhombus.

• Formula for the Dirichlet kernel with the frequencies in the anisotropically dilated rhombus.

摘要

•Asymptotics of the Lebesgue constant for the Lagrange interpolation based on the Lissajous-Chebyshev node points.•Asymptotics of the Lebesgue constant for the partial sums of the Fourier series generated by the anisotropically dilated rhombus.•Formula for the Dirichlet kernel with the frequencies in the anisotropically dilated rhombus.

论文关键词：Lebesgue constants,Asymptotic formula,Anisotropy,Dirichlet kernel,Interpolation,Lissajous-Chebyshev nodes

论文评审过程：Received 23 September 2020, Revised 2 March 2021, Accepted 9 March 2021, Available online 23 March 2021, Version of Record 23 March 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126192