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Closed ideals of $$A^ +$$ and the Cantor set. (English) Zbl 0791.46027
Let $$A^ +$$ be the algebra of analytic functions in the disc whose series of Taylor coefficients at the origin is absolutely convergent. Closed ideals of $$A^ +$$ whose hull is finite or countable were characterized by Kahane and Bennett-Gilbert, and it was conjectured that any closed ideal $$I$$ of $$A^ +$$ has the form $$S_ I H^ \infty\cap I^ A$$ where $$I^ A$$ is the closed ideal $$I$$ of the Wiener algebra $$A(\Gamma)$$ generated by $$I$$ and where $$S_ I$$ is the greatest common divisor of the inner factors of the nonzero elements of $$I$$. The results of this paper show that this conjecture is true when $$h(I)\cap\Gamma$$, the intersection of the hull of $$I$$ with the unit circle $$\Gamma$$, is contained in the triadic Cantor set.

##### MSC:
 46J20 Ideals, maximal ideals, boundaries 30H05 Spaces of bounded analytic functions of one complex variable
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