【摘要】 <正> 称这处函数 f(z)为单位圆上的一个典型实照函数,记其全体为 T_r.设 f(z)是 T_r中的一个函数,f(z)映照|z|<的像是区域 D,如果对于 D 中任意一点都可以用完全落在 D 中的直线段与ω=0相联结的话,称 f(z)是一個星像的典型实照更多还原

【Abstract】 Let the function（?）with real coefficients α_υ^（κ）be regular in |z|<1,and be such that f_κ（z）mapsthe circle |z|=γ into α contour which passess through the real axles in exactly2κ points for every γ in the interval（?）.Denote thefamily of all such functions by Т_γ^κ,and write Т_γ for Т_γ¹.Any function f_κ（z）of the subclass T_γ^κ of T_γ^κ,if is such that for each γ in 1-δ<γ<1,the radius vector（?）turns continuously in the counterclockwise direction and makes κ complete revolutions as θ varies from 0 to 2π.We prove in the present note that any f_κ（z）of T_γ^κ can be represented inthe form（?）with an increasing function α（θ）satisfying（?）.By means of thisformula,we establish the following:Theorem.If f_κ（z）∈Τ_γ^κ,then（?）All these estimates are precise.A function（?）,with real coeffi-cients is said to be belonging to the subclass T_γ^κ（ρ,р）,if there exists αρ（0<<ρ<1）such that（?）The coefficients of such a function f_κ,р（z）satisfy the inequality（?）This estimate is precise.The result holds good even when α_κ+рn^（κ）（ρ,р）are notall real,if f_κ,р（z）is κ-valent and（?）更多还原