# 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}, journal={Canadian Journal of Mathematics}, year={1970}, volume={22}, pages={1266 - 1283} }

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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Let giz) = f(z)(z -a)-n~K By Proposition 4.5, g G ^4°°. For h £ I we have, again by Proposition 4.5, A(z) = (z -a) n+1 H(z), where ff G ,4 oe . Hence gh = fH £ I

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