Spectra of infinitesimal generators of composition semigroups on weighted Bergman spaces induced by doubling weights
Abstract
Suppose (Ct)t≥0 is the composition semigroup induced by a one-parameter semigroup (t)t≥0 of analytic self-maps of the unit disk. The main purpose of the paper is to investigate the spectrum of the infinitesimal generator of (Ct)t≥0 acting on the weighted Bergman space induced by doubling weights, provided (t)t≥0 is elliptic. The method applied is a certain spectral mapping theorem and a characterization of the spectra of certain composition operators. Eventual norm-continuity of (Ct)t≥0 also plays an important role, which can be depicted in terms of studying the difference of two distinct composition operators. As a byproduct, we also characterize a certain compact integral operator that is closely related to the resolvent of the infinitesimal generator of (Ct)t≥0.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.