Lacunary Trigonometric Interpolation On Equidistant Nodes

Let f(θ) ∊ C2π. and let RM(f;θ) be the unique trigonometric polynomial of degree M satisfying (1.1) on the equidistant nodes 9, • We compare the error f(6) - RM(f;θ) with the error f(θ) - L (f;8) where LM (f;θ) is the Lagrange interpolant to f on the equidistant nodes [formula omitted], n - 2m+l. As a consequence it follows that if L (f;6) converges uniformly to f, then so does RM(f;θ).