Ideals in Rings of Analytic Functions with Smooth Boundary Values
- 1 December 1970
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 22 (6) , 1266-1283
- https://doi.org/10.4153/cjm-1970-143-x
Abstract
LetAdenote the Banach algebra of functions analytic in the open unit discDand continuous in. Iffand its firstmderivatives belong toA,then the boundary functionf(eiθ)belongs toCm(∂D). The spaceAmof all such functions is a Banach algebra with the topology induced byCm(∂D).If all the derivatives of/ belong toA,then the boundary function belongs toC∞(∂D), and the spaceA∞all such functions is a topological algebra with the topology induced byC∞(∂D). In this paper we determine the structure of the closed ideals ofA∞(Theorem 5.3).Beurling and Rudin (see e.g. [7, pp. 82-89;10]) have characterized the closed ideals ofA, and their solution suggests a possible structure for the closed ideals ofA∞.Keywords
This publication has 1 reference indexed in Scilit:
- Séries de Fourier absolument convergentesPublished by Springer Nature ,1970