Crouzeix's Conjecture and related problems

Kelly Bickel; Pamela Gorkin; Anne Greenbaum; Thomas Ransford; Felix Schwenninger; Elias Wegert

doi:10.48550/arXiv.2006.04901

Crouzeix's Conjecture and related problems

Kelly Bickel, Pamela Gorkin, Anne Greenbaum, Thomas Ransford, Felix Schwenninger, Elias Wegert

Research output: Working paper › Preprint › Academic

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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.

Original language	English
Publisher	ArXiv.org
DOIs	https://doi.org/10.48550/arXiv.2006.04901
Publication status	Published - 8 Jun 2020

Keywords

math.FA
cs.NA
math.CV
math.NA
47A25, 47A12, 15A60, 47A20, 30J10

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10.48550/arXiv.2006.04901

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Crouzeix’s Conjecture and Related Problems
Bickel, K., Gorkin, P., Greenbaum, A., Ransford, T., Schwenninger, F. L. & Wegert, E., Nov 2020, In: Computational Methods and Function Theory. 20, 3-4, p. 701-728 28 p.
Research output: Contribution to journal › Article › Academic › peer-review

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Cite this

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Crouzeix's Conjecture and related problems

Abstract

Keywords

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Crouzeix’s Conjecture and Related Problems

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