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Hölder Exponents of Green’s Functions of Cantor Sets

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Abstract

We obtain improved estimates for the Hölder exponents of Green’s functions associated to Cantor ternary sets. In particular, we show that the Green’s function associated to the classical Cantor middle-third set is Hölder continuous of order at least 0.3413.

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Authors and Affiliations

  1. Département de mathématiques et de statistique, Université Laval, Québec, QC, G1K 7P4, Canada

    Thomas Ransford & Jérémie Rostand

Authors
  1. Thomas Ransford
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  2. Jérémie Rostand
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Corresponding author

Correspondence to Thomas Ransford.

Additional information

First author supported by grants from NSERC, FQRNT and the Canada Research Chairs program. Second author supported by a grant from NSERC and FQRNT.

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Ransford, T., Rostand, J. Hölder Exponents of Green’s Functions of Cantor Sets. Comput. Methods Funct. Theory 8, 151–158 (2008). https://doi.org/10.1007/BF03321678

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  • DOI: https://doi.org/10.1007/BF03321678

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