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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Linear differential equations with slowly growing solutions
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by Janne Gröhn, Juha-Matti Huusko and Jouni Rättyä PDF
Trans. Amer. Math. Soc. 370 (2018), 7201-7227 Request permission

Abstract:

This research concerns linear differential equations in the unit disc of the complex plane. In the higher order case the separation of zeros (of maximal multiplicity) of solutions is considered, while in the second order case slowly growing solutions in $H^\infty$, $\mathrm {BMOA}$, and the Bloch space are discussed. A counterpart of the Hardy–Stein–Spencer formula for higher derivatives is proved, and then applied to study solutions in the Hardy spaces.
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Additional Information
  • Janne Gröhn
  • Affiliation: Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland
  • MR Author ID: 943256
  • Email: janne.grohn@uef.fi
  • Juha-Matti Huusko
  • Affiliation: Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland
  • MR Author ID: 1156076
  • Email: juha-matti.huusko@uef.fi
  • Jouni Rättyä
  • Affiliation: Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland
  • MR Author ID: 686390
  • Email: jouni.rattya@uef.fi
  • Received by editor(s): November 14, 2016
  • Received by editor(s) in revised form: March 17, 2017
  • Published electronically: July 12, 2018
  • Additional Notes: The first author was supported in part by the Academy of Finland #286877.
    The second author was supported in part by the Academy of Finland #268009, and the Faculty of Science and Forestry of the University of Eastern Finland #930349.
    The third author was supported in part by the Academy of Finland #268009, the Faculty of Science and Forestry of University of Eastern Finland #930349, La Junta de Andalucía (FQM210) and (P09-FQM-4468), and the grants MTM2011-25502, MTM2011-26538 and MTM2014-52865-P
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 7201-7227
  • MSC (2010): Primary 30H10, 34M10
  • DOI: https://doi.org/10.1090/tran/7265
  • MathSciNet review: 3841847