Algebraic Versus Analytic Density of Polynomials
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866914849341046784 |
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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 |