Quasianalyticity in certain Banach function algebras

Feinstein, Joel; Morley, S.

Abstract

Let X be a perfect, compact subset of the complex plane. We consider algebras of those functions on X which satisfy a generalized notion of differentiability, which we call F-differentiability. In particular, we investigate a notion of quasianalyticity under this new notion of differentiability and provide some sufficient conditions for certain algebras to be quasianalytic. We give an application of our results in which we construct an essential, natural uniform algebra A on a locally connected, compact Hausdorff space X such that A admits no non-trivial Jensen measures yet is not regular. This construction improves an example of the first author (2001).

Citation

Feinstein, J., & Morley, S. (in press). Quasianalyticity in certain Banach function algebras. Studia Mathematica, 238(2), https://doi.org/10.4064/sm8614-12-2016

• Journal Article Type: Article
• Acceptance Date: Nov 21, 2016
• Online Publication Date: Mar 16, 2017
• Deposit Date: Feb 24, 2017
• Publicly Available Date: Mar 16, 2017
• Journal: Studia Mathematica
• Print ISSN: 0039-3223
• Electronic ISSN: 1730-6337
• Publisher: Polskiej Akademii Nauk, Instytut Matematyczny
• Peer Reviewed: Peer Reviewed
• Volume: 238
• Issue: 2
• DOI: https://doi.org/10.4064/sm8614-12-2016
• Keywords: Differentiable functions, Banach function algebra, Uniform algebra, Quasianalyticity, Jensen measures, Swiss cheeses
• Public URL: https://nottingham-repository.worktribe.com/output/851015
• Publisher URL: https://www.impan.pl/en/publishing-house/journals-and-series/studia-mathematica/online/92101/quasianalyticity-in-certain-banach-function-algebras