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On uniform algebras containing A(K). (English. Russian original) Zbl 0591.46045
Russ. Math. Surv. 40, No. 2, 205-206 (1985); translation from Usp. Mat. Nauk 40, No. 2, 169-170 (1985).
Let K be a compact subset of the complex plane, $$K^ 0$$ be the interior of K which consists of a finite number of components of connectedness $$G_ 1,...,G_ n$$ and $$\partial K$$ be the boundary of K. Let A(K) be the uniform algebra of all continuous functions on K which are holomorphic in $$K^ 0.$$
The description of such uniform algebras on $$\partial K$$ which contain A(K) as subalgebra is given. It is stated that A(K$$\setminus \cup^{n}_{i=1}G_ i)$$ coincides with the uniform algebra on $$\partial K$$ generated by the functions from A(K) and by the functions $$(z-z_ 1)^{-1},...,(z-z_ n)^{-1}$$, where $$z_ i\in G_ i$$ for each i.
Reviewer: M.Abel

##### MSC:
 46J10 Banach algebras of continuous functions, function algebras 46J15 Banach algebras of differentiable or analytic functions, $$H^p$$-spaces
##### Keywords:
algebras of holomorphic functions; uniform algebra
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