Quasianalyticity in certain Banach function algebras

J. F. Feinstein¹ ; S. Morley¹

¹ School of Mathematical Sciences The University of Nottingham University Park Nottingham, NG7 2RD, UK

Studia Mathematica, Tome 238 (2017) no. 2, pp. 133-153

Résumé

Let $X$ be a perfect, compact subset of the complex plane. We consider algebras of those functions on $X$ which satisfy a generalised notion of differentiability, which we call $\mathcal {F}$-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).

Détail

DOI : 10.4064/sm8614-12-2016

Keywords: perfect compact subset complex plane consider algebras those functions which satisfy generalised notion differentiability which call mathcal differentiability particular investigate notion quasianalyticity under notion differentiability provide sufficient conditions certain algebras quasianalytic application results which construct essential natural uniform algebra locally connected compact hausdorff space admits non trivial jensen measures yet regular construction improves example first author