A solution to Crouzeix's conjecture

Emiel Lorist; Felix Schwenninger

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arXiv · 2608.03841

A solution to Crouzeix's conjecture

Emiel Lorist·Felix Schwenninger

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Abstract

We provide a proof of Crouzeix's conjecture, which combines the tools developed previously for weaker estimates with a simple perturbation lemma for $2$-dilations. Applying the lemma to the iterates $f^{n}$ in the double-layer potential representation yields the conjectured bound.

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Emiel Lorist, Felix Schwenninger. 2026-08-04. A solution to Crouzeix's conjecture. https://arxiv.org/abs/2608.03841

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