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Bloch and normal functions and their relation

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Abstract

Following a brief introduction to Bloch and normal functions, several conditions, including a convergence theorem, are shown for determining them. In addition, since an exponential of any constant multiple of a Bloch function is always normal, we investigate whether or not the converse holds, and construct an example of a non-Bloch function such that the exponential of any constant multiple of it is normal.

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Author notes

  1. Flavia Colonna

    Present address: Department of Mathematical Sciences, George Mason University, 4400 University Dr., 22030, Fairfax, VA

Authors and Affiliations

  1. University of Maryland, College Park, Maryland

    Flavia Colonna

  2. Università di Bari, Bari, Italy

    Flavia Colonna

Authors
  1. Flavia Colonna
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Additional information

Research partially supported by MPI and CNR grants. This work forms part of the author's Ph.D. Dissertation [Co]. She wishes to express her gratitude to her advisor, Prof. Maurice Heins, for his help and guidance.

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Colonna, F. Bloch and normal functions and their relation. Rend. Circ. Mat. Palermo 38, 161–180 (1989). https://doi.org/10.1007/BF02843992

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  • DOI: https://doi.org/10.1007/BF02843992

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