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arXiv · 2406.18353

Algebraic Versus Analytic Density of Polynomials

Brian Simanek·Richard Wellman
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Abstract

We show that under very mild conditions on a measure $\mu$ on the real line, the span of $\{x^n\}_{n=j}^{\infty}$ is dense in $L^2(\mu)$ for any $j\in\mathbb{N}$. We also present a slightly weaker result with an interesting proof that uses Sobolev orthogonality.

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Brian Simanek, Richard Wellman. 2024-06-26. Algebraic Versus Analytic Density of Polynomials. https://arxiv.org/abs/2406.18353

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