Decay estimate of bivariate Chebyshev coefficients for functions with limited smoothness

Abstract

We obtain the decay bounds for Chebyshev series coefficients of functions with finite Vitali variation on the unit square. A generalization of the well known identity, which relates exact and approximated coefficients, obtained using the quadrature formula, is derived. Finally, an asymptotic $L^1$-approximation error of finite partial sum for functions of bounded variation in sense of Vitali as well as Hardy-Krause, on the unit square is deduced.