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Asymptotics of the Lebesgue constants for bivariate approximation processes (2009.07114v1)
Published 15 Sep 2020 in math.CA, cs.NA, and math.NA
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.