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Computational Methods and Function Theory

, Volume 6, Issue 2, pp 423–436 | Cite as

An Estimate of the Universal Means Spectrum of Conformal Mappings

  • Alan Sola
Article

Abstract

In the theory of conformal mappings, one way of measuring how much a univalent function expands or contracts the unit disk is to study the integral means of its derivative along circles of increasing radii. Recently, Hedenmalm and Shimorin were able to find estimates on the universal means spectrum of conformal maps of the unit disk by using a combination of area-type methods and Bergman space techniques. Their paper included a numerical implementation based on the first two terms in a series expansion. We take three terms into account and show that it is possible to improve the previous results slightly.

Keywords

Universal means spectrum conformal mapping Bergman spaces 

2000 MSC

30C35 32A36 

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Copyright information

© Heldermann  Verlag 2006

Authors and Affiliations

  1. 1.Department of MathematicsRoyal Institute of TechnologyStockholmSweden

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