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The maximum selection principle allows to give expansions, in an adaptive way, of functions in the Hardy space $$\mathbf H_2$$ 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 $$\mathbb C^N$$ C N , and this fact allows us to extend in the present paper the maximum...
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