Swiss Cheeses and Their Applications

Joel Feinstein; Sam Morley; Hongfei Yang

doi:10.1090/conm/645/12928

Swiss Cheeses and Their Applications

Joel Feinstein, Sam Morley, Hongfei Yang

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Citations (Scopus)

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.

Original language	English
Title of host publication	Function Spaces in Analysis
Subtitle of host publication	Papers from the 7th Conference on Function Spaces held at Southern Illinois University
Publisher	American Mathematical Society
Pages	99-118
ISBN (Print)	978-1-4704-1694-2
DOIs	https://doi.org/10.1090/conm/645/12928
Publication status	Published - 2015
Externally published	Yes

Publication series

Name	Contemporary Mathematics
Publisher	American Mathematical Society
Volume	645
ISSN (Print)	0271-4132

Access to Document

10.1090/conm/645/12928

https://arxiv.org/abs/1412.6406Licence: Unspecified

Cite this

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title = "Swiss Cheeses and Their Applications",

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.",

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Swiss Cheeses and Their Applications. / Feinstein, Joel; Morley, Sam; Yang, Hongfei.

Function Spaces in Analysis: Papers from the 7th Conference on Function Spaces held at Southern Illinois University. American Mathematical Society, 2015. p. 99-118 (Contemporary Mathematics; Vol. 645).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Morley, Sam

AU - Yang, Hongfei

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AB - 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.

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