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arXiv · 2608.14103

Extremal functions and zero sets for the Dirichlet space

Alexander Borichev·Omar El-Fallah·Karim Kellay
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Abstract

We study the zeros of functions in the Dirichlet space. Using extremal functions, we produce a necessary and sufficient condition for a sequence of points in the unit disk to be a zero set of the classical Dirichlet space. This Shapiro-Shields type condition involves kernels of the harmonic Dirichlet space associated with measures depending on the zero sequence.

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Alexander Borichev, Omar El-Fallah, Karim Kellay. 2026-08-14. Extremal functions and zero sets for the Dirichlet space. https://arxiv.org/abs/2608.14103

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