有穷正级亚纯函数的T方向和Borel.pdfVIP

502 Vol.50, No.2 20073 ACTA MATHEMATICA SINICA, Chinese Series Mar., 2007 : 0583-1431(2007)02-0413-08 : A Æ T Borel 610225 E-mail: qdzhang@cuit.edu.cn λ, q q , E = {arg z = θ |0 ≤ θ θ · · · θ 1 2 1 j 1 2 q1 2π} E2 = {arg z = φj |0 ≤ ϕ1 ϕ2 · · · ϕq2 2π}, E1 ∩ E2 = ∅, (1) λ f (z), E1 ∪ E2 T E2 Borel , (2) λ g (z), E1 ∪ E2 Borel E2 T . ; T ; Borel MR(2000) 30D35 O174.52 T Direction and Borel Direction of Meromorphic Functions of Finite and Positive Order Qing De ZHANG Department of Computational Science, Chengdu University of Information Technology, Chengdu 610225, P. R. China E-mail: qdzhang@cuit.edu.cn Abstract Let λ be a positive number, q and q be positive integers. Assume that 1 2 E1 = {arg z = θj |0 ≤ θ1 θ2 · · · θq1 2π} and E2 = {arg z = φj |0 ≤ ϕ1 ϕ2 · · · ϕq2 2π} such that E1 ∩ E2 = ∅. Then (1) there exists a meromorphic function f (z) of order λ with E1 ∪ E2 as its T direction and E2 as its Borel direction, (2) there exists a meromorphic function g (z) of order and lower order λ with E1 ∪ E2 as its Borel direction and E2 as its T direction. Keywords meromorphic functions of finite and positive order; T direction; Borel direction MR(2000) Subject Classification 30D35 Chinese Library Classification O174.52 1 [1] 2003 T . : 2005-10-28; : 2006-04-07