Schlicht solutions of $W”+pW=0$

The Schwarzian Derivative and Schlicht Functions

It is customary to formulate the inequalities of the "Verzerrungssatz" type for analytic functions w—f(z), schlicht in the unit circle, with reference to a specific normalization. The two normalizations mainly used are: (a) f(z) is finite in \z\ < 1 , /(O) = 0 , /'(O) = 1; (b) ƒ(z) has a pole at 2 = 0 with the residue 1. If we want to obtain inequalities which are independent of any particular ...

The Coefficients of Schlicht and Allied Functions

regular and schlicht (univalent) in | z | < 1, i.e. assuming distinct values w for distinct values of z. The functions f(z) e S map | z | < 1 1 : 1 conformally onto a simply connected domain D in the w plane. During the last international Congress at Harvard Professors Schaeffer and Spencer [12] reported on the progress, largely due to their own work, on the so-called coefficient problem for S,...

Schlicht regions for entire and meromorphic functions

Let f : C → C be a meromorphic function. We study the size of the maximal disc in C with respect to spherical metric, in which a singlevalued branch of f−1 exists. The problem is related to normality and type criteria. Best possible lower estimates of the size of such discs are obtained for entire functions and a class of meromorphic functions containing all elliptic functions. An estimate for ...

A Coefficient Inequality for Schlicht Functions

The Coefficient Problem for Schlicht Mappings of the Exterior of the Unit Circle

The underlying problem confronting us in this paper is the determination of precise upper bounds for the moduli of the coefficients in these normalized expansions at » for functions in the classes S and T. This problem for the first two coefficients in each class has already been solved. We note first that since 4> and / are inverse, ai= —bx and a2= —b2, so for these two cases, discussion of on...