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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2410.20813 |
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| _version_ | 1866914993341988864 |
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| author | Kozhan, Rostyslav |
| author_facet | Kozhan, Rostyslav |
| contents | We introduce Nikishin system of $r$ probability measures on the unit circle. We show that such systems satisfy the AT property and therefore normality, introduced in~\cite{KVMLOPUC}, for any multi-index $(n_1,\ldots,n_r)\in\mathbb{N}^r$ with same-parity components satisfying $n_1 \ge n_2 \ge\ldots\ge n_r$. In the case of $r=2$, we demonstrate that the same property holds without requiring $n_1 \ge n_2 \ge\ldots\ge n_r$.
The analogous simple proof works for Nikishin systems on the real line for indices satisfying $n_j\ge \max\{n_{j+1},\ldots,n_r\}-1$, $j=1,\ldots,r-1$. This is related to the proof by Cousseement and Van Assche for $r=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20813 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nikishin systems on the unit circle Kozhan, Rostyslav Classical Analysis and ODEs Spectral Theory We introduce Nikishin system of $r$ probability measures on the unit circle. We show that such systems satisfy the AT property and therefore normality, introduced in~\cite{KVMLOPUC}, for any multi-index $(n_1,\ldots,n_r)\in\mathbb{N}^r$ with same-parity components satisfying $n_1 \ge n_2 \ge\ldots\ge n_r$. In the case of $r=2$, we demonstrate that the same property holds without requiring $n_1 \ge n_2 \ge\ldots\ge n_r$. The analogous simple proof works for Nikishin systems on the real line for indices satisfying $n_j\ge \max\{n_{j+1},\ldots,n_r\}-1$, $j=1,\ldots,r-1$. This is related to the proof by Cousseement and Van Assche for $r=2$. |
| title | Nikishin systems on the unit circle |
| topic | Classical Analysis and ODEs Spectral Theory |
| url | https://arxiv.org/abs/2410.20813 |