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A Birkhoff theorem for Riemann surfaces

 

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Opened Access A Birkhoff theorem for Riemann surfaces
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Author: Montes Rodríguez, Alfonso
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 1998
Published in: Rocky Mountain Journal of Mathematics, 28 (2), 663-693.
Document type: Article
Abstract: A classical theorem of Birkhoff asserts that there exists an entire function f such that the sequence of function {/(z + n)}n≥o is dense in the space of entire functions. In this paper we give sufficient conditions on a Riemann surface R and on a given sequence {φn}n≥o of holomorphic self-mappings of R such that there exists a holomorphic function f on R such that {f o φn}n≥0 is dense in the space of holomorphic functions on R. The necessity of these conditions is examined. In particular, we characterize the Riemann surfaces R and the sequences {φn}n≥0 of automorphisms of R. for which there exists a holomorphic function f on R with the property that the sequence {f o φn] n≥o is dense in the space of the holomorphic functions on R.
Cite: Montes Rodríguez, A. (1998). A Birkhoff theorem for Riemann surfaces. Rocky Mountain Journal of Mathematics, 28 (2), 663-693.
Size: 377.3Kb
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URI: http://hdl.handle.net/11441/41843

DOI: 10.1216/rmjm/1181071794

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