Quasianalyticity in certain Banach function algebras

Feinstein, Joel and Morley, S. (2017) Quasianalyticity in certain Banach function algebras. Studia Mathematica, 238 (2). pp. 133-153. ISSN 1730-6337

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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).

Item Type: Article
Keywords: Differentiable functions, Banach function algebra, Uniform algebra, Quasianalyticity, Jensen measures, Swiss cheeses
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.4064/sm8614-12-2016
Depositing User: Eprints, Support
Date Deposited: 24 Feb 2017 13:42
Last Modified: 13 Oct 2017 01:42
URI: http://eprints.nottingham.ac.uk/id/eprint/40836

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