Adhérence faible étoile d'algèbres de fractions rationnelles
Annales de l'Institut Fourier, Tome 24 (1974) no. 4, pp. 93-120.

Étant donnés un compact K du plan complexe, et une mesure non nulle sur K, on étudie H(μ), l’adhérence dans L(μ), pour la topologie σ(L(μ),L1(μ)), de l’algèbre des fractions rationnelles d’une variable complexe, à pôles hors de K. Le résultat principal obtenu est qu’il existe un sous-ensemble Eμ de K, éventuellement vide, mesurable pour la mesure de Lebesgue plane, et une mesure μs, éventuellement nulle, absolument continue par rapport à la mesure μ, tels que : H(μ) soit isométriquement isomorphe à H(λEμ)L(μs), où λEμ désigne la restriction à Eμ de la mesure de Lebesgue plane.

Let K be a compact subset of the complex plane, and μ a measure on K; we study H(μ), the weak star closure in L(μ), of the algebra of rational functions with poles off K. The main result is the following: there exists a subset Eμ of K, possibly empty, measurable with respect to the Lebesgue measure, and a measure μs, possibly equal to zero, absolutely continuous with respect to the measure μ, such that: H(μ) is isometrically isomorphic to H(λEμ)L(μs), with λEμ the restriction to Eμ of the Lebesgue measure.

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     title = {Adh\'erence faible \'etoile d'alg\`ebres de fractions rationnelles},
     journal = {Annales de l'Institut Fourier},
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Chaumat, Jacques. Adhérence faible étoile d'algèbres de fractions rationnelles. Annales de l'Institut Fourier, Tome 24 (1974) no. 4, pp. 93-120. doi : 10.5802/aif.533. http://archive.numdam.org/articles/10.5802/aif.533/

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