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arXiv · 2603.16295

Lower bounds in $H^2$-rational approximation to Blaschke products

Laurent Baratchart·Alexander Borichev·Sylvain Chevillard·Claire Coiffard Marre·Rachid Zarouf
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Abstract

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.

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Laurent Baratchart, Alexander Borichev, Sylvain Chevillard, Claire Coiffard Marre, Rachid Zarouf. 2026-03-17. Lower bounds in $H^2$-rational approximation to Blaschke products. https://arxiv.org/abs/2603.16295

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