Toeplitz determinants whose elements are the coefficients of univalent functions

2017/04/03 by Firoz Ali, Derek K. Thomas, Ali, Md Firoz +2
Mathematics · #Analytic and geometric function theory #Holomorphic and Operator Theory #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.1704.00657

Abstract

Let S denote the class of analytic and univalent functions in \mathbbD:=\z∈ℂ: |z|<1\ of the form f(z)= z+∑_n=2^∞a_n zⁿ. In this paper, we determine sharp estimates for the Toeplitz determinants whose elements are the Taylor coefficients of functions in S and its certain subclasses. We also discuss similar problems for typically real functions.

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