Algebraic Versus Analytic Density of Polynomials

Fuente: arXiv
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Main Authors: Simanek, Brian, Wellman, Richard
Format: Preprint
Published: 2024
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author Simanek, Brian
Wellman, Richard
author_facet Simanek, Brian
Wellman, Richard
contents We show that under very mild conditions on a measure $μ$ on the real line, the span of $\{x^n\}_{n=j}^{\infty}$ is dense in $L^2(μ)$ for any $j\in\mathbb{N}$. We also present a slightly weaker result with an interesting proof that uses Sobolev orthogonality.
format Preprint
id arxiv_https___arxiv_org_abs_2406_18353
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Algebraic Versus Analytic Density of Polynomials
Simanek, Brian
Wellman, Richard
Classical Analysis and ODEs
We show that under very mild conditions on a measure $μ$ on the real line, the span of $\{x^n\}_{n=j}^{\infty}$ is dense in $L^2(μ)$ for any $j\in\mathbb{N}$. We also present a slightly weaker result with an interesting proof that uses Sobolev orthogonality.
title Algebraic Versus Analytic Density of Polynomials
topic Classical Analysis and ODEs
url https://arxiv.org/abs/2406.18353