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Trivial Jensen measures without regularity

100%

Feinstein J.

Studia Mathematica

2001

tom 148

nr 1

67-74

In this note we construct Swiss cheeses X such that R(X) is non-regular but such that R(X) has no non-trivial Jensen measures. We also construct a non-regular uniform algebra with compact, metrizable character space such that every point of the character space is a peak point.

Swiss cheeses, rational approximation and universal plane curves

63%

Feinstein J., Heath M.

Studia Mathematica

2010

tom 196

nr 3

289-306

We consider the compact plane sets known as Swiss cheese sets, which are a useful source of examples in the theory of uniform algebras and rational approximation. We develop a theory of allocation maps connected to such sets and we use this theory to modify examples previously constructed in the literature to obtain examples homeomorphic to the Sierpiński carpet. Our techniques also allow us to avoid certain technical difficulties in the literature.

Ograniczanie wyników

2 Studia Mathematica

2 Feinstein J.

1 Heath M.

1 2010

1 2001

Wyniki wyszukiwania

Trivial Jensen measures without regularity

Swiss cheeses, rational approximation and universal plane curves