Bers-orlicz spaces on the product riemann surface |
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Authors: | Ma Jigang He Yuzan |
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Affiliation: | (1) Department of Applied Mathematics, Chengdu University of Science and Technology, 610065 Chengdu, China;(2) Institute of Mathematics, Academia Sinica, 100080 Beijing, China |
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Abstract: | In this paper, the Bers-Orlicz spaces on the automorphic formA α ϕ (G) (orEA α ϕ (G)) andL α ϕ (G) on the product Riemann surfaces are studied. We prove that eachf∈A α ϕ (G) is a cusp form. Forf∈A α ϕ (G), we give the reproducing formula. And, we give the projective operatorP gga fromL α ϕ (G) toA α ϕ (G) toEA α ϕ (G)). After giving some fundamental properties of the Poincaré series, we prove a dual theoremA α ϕ (G)=(EA α ϕ (G)). Supported by the National Nature Science Foundation of China |
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