The analytic Denjoy-Carleman algebras
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Autores: Joaquim Bruna i Floris
- Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 30, Fasc. 3, 1979, págs. 213-225
- Idioma: español
- Títulos paralelos:
- Las álgebras de Denjoy-Carleman analíticas
- Enlaces
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Resumen
Classes Em of Cinifin-functions of a real variable defined by growth restrictions on its derivatives are studies in [4] in the non quasi-analytic case. In this paper we study the analytic case, i.e. the case all functions in Em are entire. We first give a necessary and sufficient condition in order that the fact f e Em can be stated in terms of the Taylor development of f at 0. After this we see that the growth restrictions also hold for the complex derivatives and, with an auxiliary hypothesis, we show that EM can be described in terms of radial growth. In fact, the classes EM turn out to be algebras of entire functions of minimal type with respect to a given weight. From this point on, results concerning closed ideals, systems of generators, can be obtained using the same techniques as those that can be found in the literature in case of normal type.
