Embedding dimension of the Dirichlet space

Michael Hartz

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arXiv · 2107.12941

Embedding dimension of the Dirichlet space

Michael Hartz

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Abstract

The classical Dirichlet space is a complete Pick space, hence by a theorem of Agler and McCarthy, there exists an embedding $b$ of the unit disc into a $d$-dimensional ball such that composition with $b$ realizes the Dirichlet space as a quotient of the Drury-Arveson space. We show that $d =\infty$ is necessary, even if we only demand that composition with $b$ induces a surjective map between the multiplier algebras.

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Michael Hartz. 2021-07-27. Embedding dimension of the Dirichlet space. https://arxiv.org/abs/2107.12941

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