Recovering Dirichlet coefficients from even samples

Abstract

In this work, we determine the exact case error for recovering a Dirichlet coefficient from finitely many positive even samples with bounded additive errors. For sequences with a bounded tail and an unrestricted initial block, a polynomial estimator is minimax among all recovery maps. Its tail and noise constants admit explicit product formulas. We prove a sharp tail asymptotic on the index scale K^(3/2) and give a terminating procedure for selecting the sample count from a computable error bound.