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Series with general exponents

Daniel E. Loeb
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Abstract

We define the Artinian and Noetherian algebra which consist of formal series involving exponents which are not necessarily integers. All of the usual operations are defined here and characterized. As an application, we compute the algebra of symmetric functions with nonnegative real exponents. The applications to logarithmic series and the Umbral calculus are deferred to another paper. On définit ici les algèbres Artinienne et Noetherienne comme étant des algèbres constituées des séries formelles à exposants pas nécessairement entiers. On definit sur ces algèbres toutes les opérations classiques et on les caracterise. Comme exemple d'exploitation de cette théorie, on s'interesse à algèbre de fonctions symétriques &agrave exponsants rèels en nonnégatifs. Une autre publication est consacrée aux applications aux series logarithmiques et au calcul ombral.

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Daniel E. Loeb. 1995-02-09. Series with general exponents. https://arxiv.org/abs/math/9502216

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