Research Repository

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A general method for constructing essential uniform algebras (2018)
Journal Article
Feinstein, J. F., & Izzo, A. J. (2018). A general method for constructing essential uniform algebras. Studia Mathematica, 246, 47-61. doi:10.4064/sm170907-23-2

A general method for constructing essential uniform algebras with prescribed properties is presented. Using the method, the following examples are constructed: an essential, natural, regular uniform algebra on the closed unit disc; an essential, natu... Read More

Quasianalyticity in certain Banach function algebras (2017)
Journal Article
Feinstein, J., & Morley, S. (in press). Quasianalyticity in certain Banach function algebras. Studia Mathematica, 238(2), doi:10.4064/sm8614-12-2016. ISSN 0039-3223

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 quasianalytici... Read More

Abstract Swiss cheese space and classicalisation of Swiss cheeses (2016)
Journal Article
Feinstein, J., Morley, S., & Yang, H. (2016). Abstract Swiss cheese space and classicalisation of Swiss cheeses. Journal of Mathematical Analysis and Applications, 438(1), doi:10.1016/j.jmaa.2016.02.004. ISSN 0022-247X

Swiss cheese sets are compact subsets of the complex plane obtained by deleting a sequence of open disks from a closed disk. Such sets have provided numerous counterexamples in the theory of uniform algebras. In this paper, we introduce a topological... Read More

Swiss cheeses and their applications (2015)
Book Chapter
Feinstein, J., Morley, S., & Yang, H. (2015). Swiss cheeses and their applications. In K. Jarosz (Ed.), Function Spaces in AnalysisAmerican Mathematical Society. doi:80.1090/conm/645/

Swiss cheese sets have been used in the literature as useful examples in the study of rational approximation and uniform algebras. In this paper, we give a survey of Swiss cheese constructions and related results. We describe some notable examples of... Read More

Removability of exceptional sets for differentiable and Lipschitz functions (2015)
Journal Article
Craig, J., Feinstein, J., & Patrick, P. (2015). Removability of exceptional sets for differentiable and Lipschitz functions. 00 Journal not listed, 645, doi:10.1090/conm/645

We discuss removability problems concerning differentiability and pointwise Lipschitz conditions for functions of a real variable. We prove that, in each of the settings under consideration, a set is removable if and only if it has no perfect subsets... Read More

Partial regularity and t-analytic sets for Banach function algebras (2011)
Journal Article
Feinstein, J., & Mortini, R. (2012). Partial regularity and t-analytic sets for Banach function algebras. Mathematische Zeitschrift, 271(1-2), doi:10.1007/s00209-011-0856-0. ISSN 0025-5874

In this note we introduce the notion of t-analytic sets. Using this concept, we construct a class of closed prime ideals in Banach function algebras and discuss some problems related to Alling’s conjecture in H infinity. A description of all closed t... Read More

Normed algebras of differentiable functions on compact plane sets (2010)
Journal Article
Dales, H., & Feinstein, J. (2010). Normed algebras of differentiable functions on compact plane sets. Indian Journal of Pure and Applied Mathematics, 41(1), doi:10.1007/s13226-010-0005-1. ISSN 0019-5588

We investigate the completeness and completions of the normed algebras (D(1)(X),∥•∥) for perfect, compact plane sets X. In particular, we construct a radially self-absorbing, compact plane set X such that the normed algebra (D(1)(X),∥•∥) is not compl... Read More

Spectral synthesis and topologies on ideal spaces for Banach *-algebras (2002)
Journal Article
Feinstein, J., Kaniuth, E., & Somerset, D. (2002). Spectral synthesis and topologies on ideal spaces for Banach *-algebras. Journal of Functional Analysis, 196(1), doi:10.1006/jfan.2002.3964. ISSN 0022-1236

This paper continues the study of spectral synthesis and the topologies τ∞ and τr on the ideal space of a Banach algebra, concentrating on the class of Banach *-algebras, and in particular on L1-group algebras. It is shown that if a group G is a fini... Read More