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Swiss Cheeses and Their Applications

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Abstract

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 Swiss cheese sets in the literature. We explain the various abstract notions of Swiss cheeses, and how they can be manipulated to obtain desirable properties. In particular, we discuss the Feinstein-Heath classicalisation theorem and related results. We conclude with the construction of a new counterexample to a conjecture of S. E. Morris, using a classical Swiss cheese set.

Details

Original languageEnglish
Title of host publicationFunction Spaces in Analysis
Subtitle of host publicationPapers from the 7th Conference on Function Spaces held at Southern Illinois University
PublisherAmerican Mathematical Society
Pages99-118
ISBN (Print)978-1-4704-1694-2
DOIs
Publication statusPublished - 2015
Externally publishedYes

Publication series

NameContemporary Mathematics
PublisherAmerican Mathematical Society
Volume645
ISSN (Print)0271-4132

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ID: 142543032

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