Asymptotics of the Lebesgue constants for bivariate approximation processes

In this paper asymptotic formulas are given for the Lebesgue constants generated by three special approximation processes related to the l(1) -partial sums of Fourier series. In particular, we consider the Lagrange interpolation polynomials based on the Lissajous-Chebyshev node points, the partial sums of the Fourier series generated by the anisotropically dilated rhombus, and the corresponding discrete partial sums. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper presents asymptotic formulas for the Lebesgue constants generated by three special approximation processes related to the l(1) -partial sums of Fourier series, including Lagrange interpolation polynomials based on Lissajous-Chebyshev node points, the partial sums of Fourier series generated by anisotropically dilated rhombus, and the corresponding discrete partial sums.