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Spectral Notions for Conformal Maps: a Survey

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Abstract

The universal means spectrum of conformal mappings has been studied extensively in recent years. In some situations, sharp results are available, in others, only upper and lower estimates have been obtained so far. We review some of the classical results before discussing the recent work of Hedenmalm and Shimorin on estimates of the universal means spectrum near the origin. It is our ambition to explain how their method works and what its limitations are. We then move on to the recent study of the universal means spectrum of bounded functions near the point 2 conducted by Baranov and Hedenmalm. A number of open problems related to these topics are pointed out.

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Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden

    Håkan Hedenmalm & Alan Sola

Authors
  1. Håkan Hedenmalm
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  2. Alan Sola
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Correspondence to Håkan Hedenmalm.

Additional information

Research supported by the Göran Gustafsson Foundation and the Knut & Alice Wallenberg Foundation.

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Hedenmalm, H., Sola, A. Spectral Notions for Conformal Maps: a Survey. Comput. Methods Funct. Theory 8, 447–474 (2008). https://doi.org/10.1007/BF03321698

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