2021/11/15 by Jessica Doctor, Timothy J. Hodges, Doctor, Jessica +7
Mathematics · #47B33 #Advanced Harmonic Analysis Research #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2111.07853
openalex publication_date 2021/11/15 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
Previously, spectra of certain weighted composition operators on the Hardy Space were discovered under one of two hypotheses: either the compositional symbol converges under iteration to the Denjoy-Wolff point on all of the open disk rather than compact subsets, or the compositional symbol is "essentially linear fractional". We show that if the symbol is a quadratic self-map of the disk of parabolic type, then the spectrum of the weighted composition operators can be found when these maps exhibit both of the aforementioned properties, and most of them do.