On a density problem related to a theorem of Szegő
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912702424678400 |
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| author | Paulsen, Chiara |
| author_facet | Paulsen, Chiara |
| contents | A classical theorem of Szegő states that for any probability measure $μ=w\frac{\mathrm{d}θ}{2π}+μ_s$ on the unit circle the polynomials are dense in $L^2(\mathbb{T},μ)$ if and only if $\log(w)\notin L^1(\mathbb{T})$. A related question asks whether the monomials with exponents in some subset $Λ\subseteq \mathbb{N}_0$ already span $L^2(\mathbb{T},μ)$ if $\log(w)\notin L^1(\mathbb{T})$. A result by Olevskii and Ulanovskii gives an answer if $μ$ belongs to a class of absolutely continuous measures. We investigate the same question for Markoff measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08739 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a density problem related to a theorem of Szegő Paulsen, Chiara Classical Analysis and ODEs Complex Variables Probability 42C05, 60G25 A classical theorem of Szegő states that for any probability measure $μ=w\frac{\mathrm{d}θ}{2π}+μ_s$ on the unit circle the polynomials are dense in $L^2(\mathbb{T},μ)$ if and only if $\log(w)\notin L^1(\mathbb{T})$. A related question asks whether the monomials with exponents in some subset $Λ\subseteq \mathbb{N}_0$ already span $L^2(\mathbb{T},μ)$ if $\log(w)\notin L^1(\mathbb{T})$. A result by Olevskii and Ulanovskii gives an answer if $μ$ belongs to a class of absolutely continuous measures. We investigate the same question for Markoff measures. |
| title | On a density problem related to a theorem of Szegő |
| topic | Classical Analysis and ODEs Complex Variables Probability 42C05, 60G25 |
| url | https://arxiv.org/abs/2511.08739 |