The region of analytic functions for the convergence of trigonometric interpolation Original Research Article

For r>0r>0 let AP(Dr)AP(Dr) denote the set of 2π2π-periodic functions which are analytic on the closed rectangle Dr={z∈C:0≤Re z≤2π,|Im z|≤r}Dr={z∈C:0≤Re z≤2π,|Im z|≤r}, and let AP[0,2π]=AP(D0)AP[0,2π]=AP(D0). For a positive integer nn let Zn={tn,1,tn,2,…,tn,n}Zn={tn,1,tn,2,…,tn,n} be a set of nodes in the interval [0,2π)[0,2π) such that tn,10r>0 such that the sequence View the MathML source(TnZf) converges to ff uniformly on [0,2π][0,2π] for every f∈AP(Dr)f∈AP(Dr) and every sequence of nodal sets ZnZn which satisfy equation (∗). The main results are summarized as View the MathML source