Compact composition operators with symbol a universal covering map

Jones, Matthew ORCID: (2015) Compact composition operators with symbol a universal covering map. Journal of Functional Analysis, 268 (4) . pp. 887-901. ISSN 0022-1236 (doi:10.1016/j.jfa.2014.11.003)

PDF - Final accepted version (with author's formatting)
Download (194kB) | Preview


In this paper we study composition operators, Cϕ, acting on the Hardy spaces that have symbol, ϕ , a universal covering map of the disk onto a finitely connected domain of the form D0\{p1,…,pn}, where D0 is simply connected and pi, i=1,…,ni=1,…,n, are distinct points in the interior of D0. We consider, in particular, conditions that determine compactness of such operators and demonstrate a link with the Poincare series of the uniformizing Fuchsian group. We show that Cϕ is compact if, and only if ϕ does not have a finite angular derivative at any point of the unit circle, thereby extending the result for univalent and finitely multivalent ϕ.

Item Type: Article
Additional Information: Available online 18 November 2014.
Research Areas: A. > School of Science and Technology > Design Engineering and Mathematics
Item ID: 13840
Useful Links:
Depositing User: Matthew Jones
Date Deposited: 31 Oct 2014 15:57
Last Modified: 02 Jun 2019 11:13

Actions (login required)

Edit Item Edit Item

Full text downloads (NB count will be zero if no full text documents are attached to the record)

Downloads per month over the past year