Asymptotics of the Lebesgue constants for bivariate approximation processes

Abstract

In this paper asymptotic formulas are given for the Lebesgue constants generated by three special approximation processes related to the ℓ1-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.