Lower bounds in $H^2$-rational approximation to Blaschke products
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917349882331136 |
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| author | Baratchart, Laurent Borichev, Alexander Chevillard, Sylvain Marre, Claire Coiffard Zarouf, Rachid |
| author_facet | Baratchart, Laurent Borichev, Alexander Chevillard, Sylvain Marre, Claire Coiffard Zarouf, Rachid |
| contents | We derive lower bounds in best rational approximation of given degree to finite Blaschke products, in the Hardy space $H^2$ of the unit disk. We first consider approximation to $z^N$, and then move on to more general Blaschke products whose zeros are bounded away from the circle. The latter case depends on Fourier coefficients estimates for Blaschke products which are of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16295 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lower bounds in $H^2$-rational approximation to Blaschke products Baratchart, Laurent Borichev, Alexander Chevillard, Sylvain Marre, Claire Coiffard Zarouf, Rachid Classical Analysis and ODEs We derive lower bounds in best rational approximation of given degree to finite Blaschke products, in the Hardy space $H^2$ of the unit disk. We first consider approximation to $z^N$, and then move on to more general Blaschke products whose zeros are bounded away from the circle. The latter case depends on Fourier coefficients estimates for Blaschke products which are of independent interest. |
| title | Lower bounds in $H^2$-rational approximation to Blaschke products |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2603.16295 |