Closed ideals in certain Beurling algebras, and synthesis of hyperdistributions

J. Esterle

ArticleOriginal scientific text

Title

Closed ideals in certain Beurling algebras, and synthesis of hyperdistributions

Authors ¹

Affiliations

Laboratoire de Mathématiques Pures, ERS 0127, Université Bordeaux I, 351, Cours de la Libération, 33405 Talence Cedex, France

Abstract

We consider the ideal structure of two topological Beurling algebras which arise naturally in the study of closed ideals of

A^{+}

. Even in the case of closed ideals I such that

h (I) = E_{\frac{1}{p}}

, the perfect symmetric set of constant ratio 1/p, some questions remain open, despite the fact that closed ideals J of

A^{+}

such that

h (J) = E_{\frac{1}{p}}

can be completely described in terms of inner functions. The ideal theory of the topological Beurling algebras considered in this paper is related to questions of synthesis for hyperdistributions such that

lim \supset_{n \to - \infty}

|\hatφ(n)| < ∞

and s u c h t \hat{}

lim sup_{n→∞} (log^{+}|\hatφ(n)|)/√n < ∞!$!.

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Title

Closed ideals in certain Beurling algebras, and synthesis of hyperdistributions

Affiliations

Abstract

Bibliography