Let f（x） be a continuous function with 2π-period i. e. f∈C2π, and let a0/2+ sum form k=1 to ∞ （akcoskx+bksinkx） （1） be its Fourier series. Sn（f）=Sn（f,x） denotes the n-th partial sum of （1）, and En（f）...Let f（x） be a continuous function with 2π-period i. e. f∈C2π, and let a0/2+ sum form k=1 to ∞ （akcoskx+bksinkx） （1） be its Fourier series. Sn（f）=Sn（f,x） denotes the n-th partial sum of （1）, and En（f）, the best approximation of f by trigonometric polynomials of order at most n. L. Leindler in his recent paper raised the following two problems. （Ⅰ） Let p>0 and let r be a nonnegative integer. Is展开更多
文摘Let f（x） be a continuous function with 2π-period i. e. f∈C2π, and let a0/2+ sum form k=1 to ∞ （akcoskx+bksinkx） （1） be its Fourier series. Sn（f）=Sn（f,x） denotes the n-th partial sum of （1）, and En（f）, the best approximation of f by trigonometric polynomials of order at most n. L. Leindler in his recent paper raised the following two problems. （Ⅰ） Let p>0 and let r be a nonnegative integer. Is
