Constructive Approximation under Carleman's Condition, with Applications to Smoothed Analysis

Frederic Koehler, Beining Wu

A classical result of Carleman, based on the theory of quasianalytic functions, shows that polynomials are dense in $L^2(\hat{I}¼)$ for any $\hat{I}¼$ such that the moments $\int x^{k}d\hat{I}¼$ do n…