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Swiss Cheeses and Their Applications

Feinstein, Joel; Morley, S.; Yang, H.

Authors

S. Morley

H. Yang



Contributors

Krzysztof Jarosz
Editor

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.

Start Date May 20, 2014
Publication Date Oct 30, 2015
Journal Contemporary Mathematics
Peer Reviewed Peer Reviewed
Volume 645
Series ISSN 1098-3627
Book Title Function Spaces in Analysis
Chapter Number 9
ISBN 978-1-4704-1694-2
APA6 Citation Feinstein, J., Morley, S., & Yang, H. (2015). Swiss Cheeses and Their Applications. In K. Jarosz (Ed.), Function Spaces in Analysishttps://doi.org/80.1090/conm/645/
DOI https://doi.org/80.1090/conm/645/
Keywords Functional Analysis;
Publisher URL http://www.ams.org/books/conm/645
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf






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