Spectra of Weighted Composition Operators with Quadratic Symbols

Authors

Derek Thompson, Taylor UniversityFollow
Jessica Doctor
Timothy Hodges
Alexander McFarland
Scott Kaschner

Document Type

Article

Publication Date

2021

Abstract

Previously, spectra of certain weighted composition operators on the Hardy space were determined under one of two hypotheses: either the compositional symbol converges under iteration to the Denjoy-Wolff point uniformly on the entire open unit disk rather than simply on compact subsets, or it is “essentially linear fractional.” We show that if the compositional symbol is a quadratic self-map of the open disk of parabolic type, then the spectrum of associated weighted composition operators can be found when these maps exhibit both of the aforementioned properties, and we determine which symbols do so.

Notes

Faculty Sponsor: Dr. Derek Thompson

Funding Source: CURM grant from NSF

Article Preprint available.

Recommended Citation

Thompson, Derek; Doctor, Jessica; Hodges, Timothy; McFarland, Alexander; and Kaschner, Scott, "Spectra of Weighted Composition Operators with Quadratic Symbols" (2021). Mathematics Student Projects. 2.
https://pillars.taylor.edu/mathstudentscholarship/2