Absolutely Continuous Representing Measures of Moment Sequences with an Emphasis on the Regularity of the Densities
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910721797783552 |
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| author | di Dio, Philipp J. |
| author_facet | di Dio, Philipp J. |
| contents | In this work we investigate and characterize linear functionals $L:\mathbb{R}[x_1,\dots,x_n]\to\mathbb{R}$ with absolutely continuous representing measures $μ$, i.e., $\mathrm{d}μ(x) = g(x)\,\mathrm{d} x$ for some density $g$. We focus on the regularity of $g$ and how it is influenced/determined by the moments $s_α= L(x^α)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03145 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Absolutely Continuous Representing Measures of Moment Sequences with an Emphasis on the Regularity of the Densities di Dio, Philipp J. Functional Analysis Algebraic Geometry 44A60, 30E05, 26C05 In this work we investigate and characterize linear functionals $L:\mathbb{R}[x_1,\dots,x_n]\to\mathbb{R}$ with absolutely continuous representing measures $μ$, i.e., $\mathrm{d}μ(x) = g(x)\,\mathrm{d} x$ for some density $g$. We focus on the regularity of $g$ and how it is influenced/determined by the moments $s_α= L(x^α)$. |
| title | Absolutely Continuous Representing Measures of Moment Sequences with an Emphasis on the Regularity of the Densities |
| topic | Functional Analysis Algebraic Geometry 44A60, 30E05, 26C05 |
| url | https://arxiv.org/abs/2411.03145 |