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Mean growth and geometric zero distribution of solutions of linear differential equations

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Abstract

The aim of this paper is to consider certain conditions on the coefficient A of the differential equation f″ + Af = 0 in the unit disc which place all normal solutions f in the union of Hardy spaces or result in the zero-sequence of each non-trivial solution being uniformly separated. The conditions on the coefficient are given in terms of Carleson measures.

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Authors and Affiliations

  1. Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101, Joensuu, Finland

    Janne Gröhn & Jouni Rättyä

  2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Spain

    Artur Nicolau

Authors
  1. Janne Gröhn
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  2. Artur Nicolau
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  3. Jouni Rättyä
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Corresponding author

Correspondence to Janne Gröhn.

Additional information

Supported by the Academy of Finland #258125 and #286877.

Supported in part by the grants MTM2014-51824-P, MTM2017-85666-P, and 2014SGR 75.

Supported in part by the Academy of Finland #268009, by the Faculty of Science and Forestry of University of Eastern Finland #930349, and by the grant MTM2011-26538.

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Gröhn, J., Nicolau, A. & Rättyä, J. Mean growth and geometric zero distribution of solutions of linear differential equations. JAMA 134, 747–768 (2018). https://doi.org/10.1007/s11854-018-0024-0

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  • DOI: https://doi.org/10.1007/s11854-018-0024-0

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