Quasianalyticity in certain Banach function algebras
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...
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| Format: | Article |
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Polish Academy of Sciences, Institute of Mathematics
2017
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| Online Access: | https://eprints.nottingham.ac.uk/40836/ |
| _version_ | 1848796143757033472 |
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| author | Feinstein, Joel Morley, S. |
| author_facet | Feinstein, Joel Morley, S. |
| author_sort | Feinstein, Joel |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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). |
| first_indexed | 2025-11-14T19:43:18Z |
| format | Article |
| id | nottingham-40836 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:18Z |
| publishDate | 2017 |
| publisher | Polish Academy of Sciences, Institute of Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-408362020-05-04T18:38:04Z https://eprints.nottingham.ac.uk/40836/ Quasianalyticity in certain Banach function algebras Feinstein, Joel Morley, S. 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). Polish Academy of Sciences, Institute of Mathematics 2017-03-16 Article PeerReviewed Feinstein, Joel and Morley, S. (2017) Quasianalyticity in certain Banach function algebras. Studia Mathematica, 238 (2). pp. 133-153. ISSN 1730-6337 Differentiable functions Banach function algebra Uniform algebra Quasianalyticity Jensen measures Swiss cheeses https://www.impan.pl/en/publishing-house/journals-and-series/studia-mathematica/online/92101/quasianalyticity-in-certain-banach-function-algebras doi:10.4064/sm8614-12-2016 doi:10.4064/sm8614-12-2016 |
| spellingShingle | Differentiable functions Banach function algebra Uniform algebra Quasianalyticity Jensen measures Swiss cheeses Feinstein, Joel Morley, S. Quasianalyticity in certain Banach function algebras |
| title | Quasianalyticity in certain Banach function algebras |
| title_full | Quasianalyticity in certain Banach function algebras |
| title_fullStr | Quasianalyticity in certain Banach function algebras |
| title_full_unstemmed | Quasianalyticity in certain Banach function algebras |
| title_short | Quasianalyticity in certain Banach function algebras |
| title_sort | quasianalyticity in certain banach function algebras |
| topic | Differentiable functions Banach function algebra Uniform algebra Quasianalyticity Jensen measures Swiss cheeses |
| url | https://eprints.nottingham.ac.uk/40836/ https://eprints.nottingham.ac.uk/40836/ https://eprints.nottingham.ac.uk/40836/ |