A solution to Crouzeix's conjecture
Preprint
(2026)
Author(s)
E. Lorist (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Felix Schwenninger (University of Twente)
Research Group
Analysis
DOI related publication
https://doi.org/10.48550/arXiv.2608.03841
Final published version
To reference this document use
https://resolver.tudelft.nl/uuid:ccd0abd4-5787-4a44-a6b1-b2bc4e28c147
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Publication Year
2026
Language
English
Research Group
Analysis
Page Views
10
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 fn in the doublelayer
potential representation yields the conjectured bound.