On the estimate of the fourth-order homogeneous coefficient functional for univalent functions

Gromova, Larisa; Vasil'ev, Alexander

doi:10.4064/ap-63-1-7-12

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Changing the Order Of Integration Implies1

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2007

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“…In general, the polynomials P k are homogeneous with respect to rotations of the function f . It is worthy to mention that estimates of the absolute value of these polynomials has been a subject of investigations in the theory of univalent functions for a long time, e.g., for |P 2 | we have |c 3 − c 2 2 | ≤ 1 (Bieberbach 1916 [3]), for estimates of |P 3 | see [7,14,23,24]. For the Neretin polynomials one can construct the generatrix function…”

Section: Changing the Order Of Integration Impliesmentioning

confidence: 99%

Energy characteristics of subordination chains

Vasil'ev

2007

Ark. Mat.

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We consider subordination chains of simply connected domains with smooth boundaries in the complex plane. Such chains admit Hamiltonian and Lagrangian interpretations through the Löwner-Kufarev evolution equations. The action functional is constructed and its time variation is obtained. It represents the infinitesimal version of the action of the Virasoro-Bott group over the space of analytic univalent functions.

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Section: Changing the Order Of Integration Impliesmentioning

confidence: 99%