Spectral properties of weighted composition semigroups on the Bloch space
Date
2019-08
Authors
Mose, Samuel
Bonyo, Job
Okoth, Isaac
Journal Title
Journal ISSN
Volume Title
Publisher
Strathmore University
Abstract
We determine both the semigroup and spectral properties of a group of weighted SBS
composition operators on the Little Bloch space. It turns out that these are strongly continuous
groups of invertible isometries on the Bloch space. We then obtain the norm and spectra of the
infinitesimal generator as well as the resulting resolvents which are given as integral operators.
Using the spectral mapping theorem as well as the Hille Yosida theorem we obtain the spectral
properties of the resulting integral operators.
Description
Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, Kenya
Keywords
Analytic functions, Non-reflexive Bergman space, Spectrum and resolvent