Swiss Cheeses and Their Applications

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

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.

Citation

Feinstein, J., Morley, S., & Yang, H. (2015). Swiss Cheeses and Their Applications. In K. Jarosz (Ed.), Function Spaces in Analysis. https://doi.org/80.1090/conm/645/

• Conference Name: Seventh Conference on Function Spaces
• Conference Location: Southern Illinois University at Edwardsville
• Start Date: May 20, 2014
• End Date: May 24, 2019
• Acceptance Date: Jun 10, 2015
• Online Publication Date: Oct 30, 2015
• Publication Date: Oct 30, 2015
• Deposit Date: Mar 14, 2016
• Publicly Available Date: Mar 14, 2016
• 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
• DOI: https://doi.org/80.1090/conm/645/
• Keywords: Functional Analysis
• Public URL: https://nottingham-repository.worktribe.com/output/762890
• Publisher URL: http://www.ams.org/books/conm/645