On the entropy for indeterminate moment problems
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908724488044544 |
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| author | Berg, Christian |
| author_facet | Berg, Christian |
| contents | For an indeterminate Hamburger moment problem we consider an infinite family of analytic densities solving the moment problem and we prove that they all have finite (Shannon) entropy. These densities are either all bounded or all unbounded. The result is illustrated by the Al-Salam--Carlitz moment problem, where all the densities in the family are bounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12684 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the entropy for indeterminate moment problems Berg, Christian Probability Classical Analysis and ODEs Dynamical Systems 44A60, 30D15 For an indeterminate Hamburger moment problem we consider an infinite family of analytic densities solving the moment problem and we prove that they all have finite (Shannon) entropy. These densities are either all bounded or all unbounded. The result is illustrated by the Al-Salam--Carlitz moment problem, where all the densities in the family are bounded. |
| title | On the entropy for indeterminate moment problems |
| topic | Probability Classical Analysis and ODEs Dynamical Systems 44A60, 30D15 |
| url | https://arxiv.org/abs/2511.12684 |