Ideals in Rings of Analytic Functions with Smooth Boundary Values

Taylor, B. A. ; Williams, D. L.

Canadian journal of mathematics, Tome 22 (1970) no. 6, pp. 1266-1283

Résumé

Let A denote the Banach algebra of functions analytic in the open unit disc D and continuous in . If f and its first m derivatives belong to A, then the boundary function f(eiθ) belongs to Cm(∂D). The space Am of all such functions is a Banach algebra with the topology induced by Cm(∂D). If all the derivatives of/ belong to A, then the boundary function belongs to C∞(∂D), and the space A∞ all such functions is a topological algebra with the topology induced by C∞(∂D). In this paper we determine the structure of the closed ideals of A∞ (Theorem 5.3).Beurling and Rudin (see e.g. [7, pp. 82-89; 10]) have characterized the closed ideals of A, and their solution suggests a possible structure for the closed ideals of A ∞.

Détail

DOI : 10.4153/CJM-1970-143-x

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