Two results on polynomial interpolation in equally spaced points

We present two results that quantify the poor behavior of polynomial interpolation in n equally spaced points. First, in band-limited interpolation of complex exponential functions eiαx (α ϵ R), the error decreases to 0 as n → ∞ if and only if α is small enough to provide at least six points per wavelength. Second, the Lebesgue constant Λn (supremum norm of the nth interpolation operator) satisfies limn → ∞ Λn1n = 2. Both of these results are more than 50 years old, but they are generally unknown to approximation theorists.