从属于指数函数的星像函数子类的四阶Toeplitz行列式

Forth-Order Toeplitz Determinant for Subclasses of Star-Like Functions Subordinate to Exponential Functions

设S^(*)_(l)表示单位圆盘D={z:z<1}内解析函数f(z)的全体,且满足f(0)=f′(0)-1=0,zf′(z)/f(z)e^(z)(z∈D).研究该函数类S^(*)_(l)的四阶Toeplitz行列式T_(4)(2),并给出其上界估计.

Let S^(*)_(l) denote the class of analytic functions f(z)in the open unit disk D={z:z<1}normalized by f(0)=f′(0)-1=0 and satisfying the condition zf′(z)/f(z)e^(z)(z∈D).We investigated[JP+1]the forth\|order Toeplitz determinant T 4(2)for this function class S^(*)_(l) and gave the upper bound estimate[JP]of the determinant T_(4)(2).