Analytic Versus Algebraic Density of Polynomials

Christian Berg, Brian Simanek, Richard Wellman

We show that under very mild conditions on a measure $\mu$ on the interval $[0,\infty )$, the span of $\{x^k{\}}_{k=n}^{\infty }$ is dense in $L^2(\mu )$ for any $n=0,1,\dots$. We present…