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arXiv · 1604.07047

Adaptative decomposition: the case of the Drury-Arveson space

Daniel Alpay·Fabrizio Colombo·Tao Qian·Irene Sabadini
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Abstract

The maximum selection principle allows to give expansions, in an adaptive way, of functions in the Hardy space $\mathbf H_2$ of the disk in terms of Blaschke products. The expansion is specific to the given function. Blaschke factors and products have counterparts in the unit ball of $\mathbb C^N$, and this fact allows us to extend in the present paper the maximum selection principle to the case of functions in the Drury-Arveson space of functions analytic in the unit ball of $\mathbb C^N$. This will give rise to an algorithm which is a variation in this higher dimensional case of the greedy algorithm. We also introduce infinite Blaschke products in this setting and study their convergence.

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Daniel Alpay, Fabrizio Colombo, Tao Qian, Irene Sabadini. 2016-04-24. Adaptative decomposition: the case of the Drury-Arveson space. https://arxiv.org/abs/1604.07047

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