单位圆内有穷正级亚纯函数的T-半径和Borel半径

T-radii and Borel radii of meromorphic functions of finite positive order in the unit disc

作者证明了对任意正数λ,正整数q_1和q_2,记E_1={argz=θ_j|0≤θ_1<θ_2<…<θ_(q_1)<2π},E_2={argz=φ_j|0≤φ_1<φ_2<…<φ_(q_2)<2π},使得E_1∩E_2=。则(ⅰ)存在单位圆内的λ级亚纯函数f(z),恰以E_1∪E_2为其T-半径且恰以E_2为其Borel半径,(ⅱ)存在单位圆内级和下级均为λ的亚纯函数g(z),恰以E_1∪E_2为其Borel半径且恰以E_2为其T-半径。

Let λ be a positive number, q_1 and q_2 be positive integers. Assume that E_1= {argz=θ_j|0≤θ_1<θ_2<…<θ_(q_1)<2π} and E_2={argz=φ_j|0≤φ_1<φ_2<…<φ_(q_2)<2π} such that E_1∩E_2=. Then (ⅰ) there exists a meromorphic function f(z) of order λ in the unit disc, which takes the E_1∩E_2 as its T-radii and E_2 as its Borel radii, (ⅱ) there exists a meromorphic function g(z) of order and lower order λ in the unit disc, which takes the E_1∪E_2 as its Borel radii and E_2 as its T-radii.