Approximation by weighted means of Walsh-Fourier series
Summary: We study the rate of approximation to functions in \(L^p\) and, in particular, in \(\text{Lip} (\alpha, p)\) by weighted means of their Walsh-Fourier series, where \(\alpha >0\) and \(1\leq p\leq \infty\). For the case \(p=\infty\), \(L^p\) is interpreted to be \(C_W\), the collection of uniformly \(W\) continuous functions over the unit interval \([0,1)\). We also note that the weighted mean kernel is quasi-positive, under fairly general conditions.
scientific article; zbMATH DE number 844394