A Loewner variational method in the theory of schlicht functions
Eberhard Michel
TL;DR
This paper introduces a Loewner variational method to compute coefficient functionals of schlicht functions, leading to improved bounds on the Milin-constant and the seventh coefficient of odd schlicht functions.
Contribution
It develops a new variational approach based on Loewner theory to calculate coefficient functionals and improves existing bounds for key constants in schlicht function theory.
Findings
Improved lower bound for the Milin-constant (0.034856)
Enhanced lower bound for the seventh coefficient of odd schlicht functions (1.006763)
Development of a new variational method for coefficient functional calculation
Abstract
A Loewner variational method is developed that allows to calculate arbitrary continuous coefficient functionals of the second, third and fourth coefficients of schlicht functions. Based on this method an improved lower bound for the Milin-constant(0.034856..) is given, as well as an improved lower bound for the maximal modulus of the seventh coefficient of odd schlicht functions(1.006763..).
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Taxonomy
TopicsChemical Thermodynamics and Molecular Structure · Analytic and geometric function theory