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Bad boundary behavior in star-invariant subspaces I

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Abstract

We discuss the boundary behavior of functions in star-invariant subspaces (BH 2)⊥, where B is a Blaschke product. Extending some results of Ahern and Clark, we are particularly interested in the growth rates of functions at points of the spectrum of B where B does not admit a derivative in the sense of Carathéodory.

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Authors and Affiliations

  1. Institut de Mathématiques de Bordeaux, Université de Bordeaux, 351 cours de la Libération, FR-33405, Talence, France

    Andreas Hartmann

  2. Department of Mathematics and Computer Science, University of Richmond, Richmond, VA, 23173, U.S.A.

    William T. Ross

Authors
  1. Andreas Hartmann
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  2. William T. Ross
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Corresponding author

Correspondence to William T. Ross.

Additional information

The first author was supported by ANR FRAB: ANR-09-BLAN-0058-02. The authors would like to thank the referee for some useful comments and a simplification.

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Hartmann, A., Ross, W.T. Bad boundary behavior in star-invariant subspaces I. Ark Mat 52, 113–134 (2014). https://doi.org/10.1007/s11512-012-0172-x

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  • DOI: https://doi.org/10.1007/s11512-012-0172-x

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