Crouzeix's Conjecture and related problems
Functional Analysis
2020-11-11 v1 Numerical Analysis
Complex Variables
Numerical Analysis
Abstract
In this paper, we establish several results related to Crouzeix's conjecture. We show that the conjecture holds for contractions with eigenvalues that are sufficiently well-separated. This separation is measured by the so-called separation constant, which is defined in terms of the pseudohyperbolic metric. Moreover, we study general properties of related extremal functions and associated vectors. Throughout, compressions of the shift serve as illustrating examples which also allow for refined results.
Keywords
Cite
@article{arxiv.2006.04901,
title = {Crouzeix's Conjecture and related problems},
author = {Kelly Bickel and Pamela Gorkin and Anne Greenbaum and Thomas Ransford and Felix Schwenninger and Elias Wegert},
journal= {arXiv preprint arXiv:2006.04901},
year = {2020}
}
Comments
24 pages