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A group theoretic interpretation of the last part of de Branges’ proof of the Bieberbach conjecture. (English) Zbl 0565.30011

A more conceptual and less computational proof is given for the last part of de Branges’ proof of the Bieberbach conjecture [cf. L. de Branges, Acta Math. 154, 137-152 (1985)], i.e. where the special functions enter and the Askey-Gasper inequality [cf. G. Gasper and R. Askey, Am. J. Math. 98, 709-737 (1976; Zbl 0355.33005)] is applied. General solutions of de Branges’ system of differential equations are brought in 1-1 correspondence first with Fourier-sine and next with spherical function expansions on the sphere \(S^ 3\). Restriction of spherical functions on \(S^ 5\) to \(S^ 3\) then finish the proof.
Reviewer: Ch.F.Dunkl

MSC:

30C50 Coefficient problems for univalent and multivalent functions of one complex variable
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

Biographic References:

de Branges, Louis

Citations:

Zbl 0355.33005
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