Algebraic Versus Analytic Density of Polynomials

2024/06/26 by Brian Simanek, Richard Wellman, Simanek, Brian +1
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2406.18353

openalex publication_date 2024/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that under very mild conditions on a measure μ on the real line, the span of \xⁿ\_n=j^∞ is dense in L²(μ) for any j∈ℕ. We also present a slightly weaker result with an interesting proof that uses Sobolev orthogonality.

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