In this paper,the Bers-Orlicz spaces on the automorphic form A_α■(G)(or EA_α■(G)) and L_α■(G)(E_α■(G))on the product Riemann surfaces are studied.We prove that each f ∈A_α■(G) is a cusp form.For f ∈A_α■(...In this paper,the Bers-Orlicz spaces on the automorphic form A_α■(G)(or EA_α■(G)) and L_α■(G)(E_α■(G))on the product Riemann surfaces are studied.We prove that each f ∈A_α■(G) is a cusp form.For f ∈A_α■(G),we give the reproducing formula.And,we give the projective operator P_αfrom L_α■(G) to A_α■(G)(or E_α■(G) to EA_α■(G)).After giving some fundamental properties of the Poincaréseries,we prove a dual theorem A_α■(G)=(EA_α■(G))~*.展开更多
基金Supported by the National Nature Science Foundation of China.
文摘In this paper,the Bers-Orlicz spaces on the automorphic form A_α■(G)(or EA_α■(G)) and L_α■(G)(E_α■(G))on the product Riemann surfaces are studied.We prove that each f ∈A_α■(G) is a cusp form.For f ∈A_α■(G),we give the reproducing formula.And,we give the projective operator P_αfrom L_α■(G) to A_α■(G)(or E_α■(G) to EA_α■(G)).After giving some fundamental properties of the Poincaréseries,we prove a dual theorem A_α■(G)=(EA_α■(G))~*.
