Article
A Birkhoff theorem for Riemann surfaces
Author/s | Montes Rodríguez, Alfonso |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 1998 |
Deposit Date | 2016-06-03 |
Published in |
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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 ... 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. |
Funding agencies | Dirección General de Investigación Científica y Técnica (DGICYT). España |
Project ID. | P93-0926 |
Citation | Montes Rodríguez, A. (1998). A Birkhoff theorem for Riemann surfaces. Rocky Mountain Journal of Mathematics, 28 (2), 663-693. |
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