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Swiss Cheeses and Their Applications | | J. F. Feinstein
; S. Morley
; H. Yang
; | | Date: |
19 Dec 2014 | | 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. | | Source: | arXiv, 1412.6406 | | Services: | Forum | Review | PDF | Favorites | |
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