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 ${\ell }_1$-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.