A disproof of a conjecture of Al Baernstein II
Ronen Peretz
TL;DR
This paper disproves a conjecture by Albert Baernstein II concerning the coefficients of circular symmetrization, showing that the conjecture does not hold in general.
Contribution
It provides a counterexample to a longstanding conjecture about the behavior of coefficients in circular symmetrization.
Findings
The conjecture is false in general cases.
Counterexamples demonstrate the limits of previous assumptions.
The result clarifies the scope of circular symmetrization properties.
Abstract
We answer a question that was asked by Albert Baernstein II, regarding the coefficients of circular symmetrization. The conjecture is not true generically.
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Taxonomy
TopicsAnalytic and geometric function theory · Advanced Algebra and Geometry · Finite Group Theory Research