# Ideals in Rings of Analytic Functions with Smooth Boundary Values

@article{Taylor1970IdealsIR,
title={Ideals in Rings of Analytic Functions with Smooth Boundary Values},
author={B. A. Taylor and D. L. Williams},
year={1970},
volume={22},
pages={1266 - 1283}
}
• Published 1 December 1970
• Mathematics
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…
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