Résumé
On dit qu’une mesure μ dans \( {\mathbb{C}^n} \) est orthogonale si elle est orthogonale aux polynômes, c.-à-d. \( \smallint \) P(z)dg(z) =0 pour tout polynôme P. L’étude des mesures orthogonales (resp. orthogonales aux fonctions rationnelles) est en liaison directe avec le problème d’approximation polynomiale (resp. rationnelle). L’absence de mesure orthogonale (resp. orthogonale aux fonctions rationnelles) non nulle à support dans un compact γ implique que toute fonction continue dans γ à valeurs complexes est approximable uniformement sur γ par des polynômes (resp. par des fonctions rationnelles) et réciproquement.
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Dinh, TC. (2000). Mesures orthogonales à support compact de longueur finie et applications. In: Dolbeault, P., Iordan, A., Henkin, G., Skoda, H., Trépreau, JM. (eds) Complex Analysis and Geometry. Progress in Mathematics, vol 188. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8436-5_11
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