A constructive proof of the Beurling-Rudin theorem

ArticleOriginal scientific text

Title

Authors ¹

Département de Mathématiques, Université de Metz, Ile du Saulcy, F-57045 Metz, France

A constructive proof of the Beurling-Rudin theorem on the characterization of the closed ideals in the disk algebra A() is given.

[Ga] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981.
[Ho] K. Hoffman, Banach Spaces of Analytic Functions, Dover Publ., New York, 1988 (reprint of the 1962 edition).
[Mo] R.Mortini, Closed and prime ideals in the algebra of bounded analytic functions, Bull. Austral. Math. Soc. 35 (1987) 213-229.
[MoRu] R. Mortini and R. Rupp, A constructive proof of the Nullstellensatz for subalgebras of A(K), Trav. Math. 3, Publ. CUL, 1991, 45-49.
[vR] M. von Renteln, A simple constructive proof of an analogue of the Corona theorem, Proc. Amer. Math. Soc. 83 (1981) 299-303.
[Ru] W. Rudin, The closed ideals in an algebra of analytic functions, Canad. Math. J. 9 (1957) 426-434.
[Rud] W. Rudin, A generalization of a theorem of Frostman, Math. Scand. 21 (1967), 136-143.
[SrWa] T. P. Srinivasan and J. K. Wang, On the closed ideals of analytic functions, Proc. Amer. Math. Soc. 16 (1965), 49-52.