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Polynomial Hulls of Sets Invariant Under an Action of the Special Unitary Group

Published online by Cambridge University Press:  20 November 2018

John T. Anderson
John T. Anderson*
Affiliation:
College of the Holy Cross, Worcester, Massachusetts
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If K is a compact subset of Cn, will denote the polynomial hull of K:

arises in the study of uniform algebras as the maximal ideal space of the algebra P(K) of uniform limits on K of polynomials (see [3]). The condition (K is polynomially convex) is a necessary one for uniform approximation on K of continuous functions by polynomials (P(K) = C(K)). If K is not polynomially convex, the question of existence of analytic structure in is of particular interest. For n = 1, is the union of K and the bounded components of C\K. The determination of in dimensions greater than one is a more difficult problem. Among the special classes of compact sets K whose polynomial hulls have been determined are those invariant under certain group actions on Cn.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 5 , 01 October 1988 , pp. 1256 - 1271
Copyright
Copyright © Canadian Mathematical Society 1988

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