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

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 E μ of K, possibly empty, measurable with respect to the Lebesgue measure, and a measure μ s , possibly equal to zero, absolutely continuous with respect to the measure μ, such that: H (μ) is isometrically isomorphic to H (λ E μ )L (μ s ), with λ E μ the restriction to E μ of the Lebesgue measure.

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),L 1 (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 E μ de K, éventuellement vide, mesurable pour la mesure de Lebesgue plane, et une mesure μ s , éventuellement nulle, absolument continue par rapport à la mesure μ, tels que : H (μ) soit isométriquement isomorphe à H (λ E μ )L (μ s ), où λ E μ désigne la restriction à E μ de la mesure de Lebesgue plane.

@article{AIF_1974__24_4_93_0,
     author = {Chaumat, Jacques},
     title = {Adh\'erence faible \'etoile d'alg\`ebres de fractions rationnelles},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {24},
     number = {4},
     year = {1974},
     pages = {93-120},
     doi = {10.5802/aif.533},
     zbl = {0287.46065},
     mrnumber = {53 \#14141},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1974__24_4_93_0}
}
Chaumat, Jacques. Adhérence faible étoile d'algèbres de fractions rationnelles. Annales de l'Institut Fourier, Volume 24 (1974) no. 4, pp. 93-120. doi : 10.5802/aif.533. http://www.numdam.org/item/AIF_1974__24_4_93_0/

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