Blaschke Products, Level Sets, and Crouzeix's Conjecture

Autor:	Bickel, Kelly, Gorkin, Pamela
Rok vydání:	2021
Předmět:	Mathematics - Functional Analysis Mathematics - Complex Variables Primary 47A12 30J10 Secondary 47A25 47B32
Druh dokumentu:	Working Paper
Popis:	We study several problems motivated by Crouzeix's conjecture, which we consider in the special setting of model spaces and compressions of the shift with finite Blaschke products as symbols. We pose a version of the conjecture in this setting, called the level set Crouzeix (LSC) conjecture, and establish structural and uniqueness properties for (open) level sets of finite Blaschke products that allow us to prove the LSC conjecture in several cases. In particular, we use the geometry of the numerical range to prove the LSC conjecture for compressions of the shift corresponding to unicritical Blaschke products of degree $4$. Comment: 33 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2112.06321 Zobrazit plný text záznamu View this record from Arxiv