论文标题
平滑度有限的功能的双变量Chebyshev系数的衰减估计值
Decay estimate of bivariate Chebyshev coefficients for functions with limited smoothness
论文作者
论文摘要
我们获得了函数的Chebyshev系列系数的衰减界限，并在单位正方形上具有有限的Vitali变化。得出了使用正交公式获得的精确和近似系数的众所周知的身份的概括。最后，推导了单位正方形上有限变化的函数和hardy-krause的有限差异函数的有限部分总和的渐近$ l^1 $ approximatimatimation误差。
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.
