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Quasianalyticity in certain Banach function algebras

Feinstein, Joel; Morley, S.

Authors

S. Morley



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 http://eprints.nottingham.ac.uk/id/eprint/40836
Publisher URL https://www.impan.pl/en/publishing-house/journals-and-series/studia-mathematica/online/92101/quasianalyticity-in-certain-banach-function-algebras
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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