Strong uniform approximation by double Fourier series
The authors study the rate of strong uniform approximation of continuous functions f(x,y), \(2\pi\)-periodic in each variable, by the rectangular partial sums of their double Fourier series. They also obtain strong approximation rates to functions in the Lipschitz classes Lip(\(\alpha\),\(\beta\)) and Zygmund classes Z(\(\alpha\),\(\beta\)), where \(\alpha\), \(\beta\in (0,1]\). Also, the approximation rates of some conjugate functions are obtained. In almost all cases, these rates are shown to be the best possible.
scientific article; zbMATH DE number 4155130
scientific article