A spectral radius type formula for approximation numbers of composition operators |
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Authors: | Daniel Li,Hervé Queffé lec,Luis Rodrí guez-Piazza |
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Affiliation: | 1. Univ Lille Nord de France, U-Artois, Laboratoire de Mathématiques de Lens EA 2462 & Fédération CNRS Nord-Pas-de-Calais FR 2956, Faculté des Sciences Jean Perrin, Rue Jean Souvraz, S.P. 18, F-62 300 Lens, France;2. Univ Lille Nord de France, USTL, Laboratoire Paul Painlevé U.M.R. CNRS 8524 & Fédération CNRS Nord-Pas-de-Calais FR 2956, F-59 655 Villeneuve d''Ascq Cedex, France;3. Universidad de Sevilla, Facultad de Matemáticas, Departamento de Análisis Matemático & IMUS, Apartado de Correos 1160, 41 080 Sevilla, Spain |
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Abstract: | For approximation numbers an(Cφ) of composition operators Cφ on weighted analytic Hilbert spaces, including the Hardy, Bergman and Dirichlet cases, with symbol φ of uniform norm <1, we prove that limn→∞?[an(Cφ)]1/n=e−1/Cap[φ(D)], where Cap[φ(D)] is the Green capacity of φ(D) in D. This formula holds also for Hp with 1≤p<∞. |
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Keywords: | primary, 47B06 secondary, 30H10, 30H20, 31A15, 47B32, 47B33 |
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