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Transactions of the American Mathematical Society

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Linear differential equations with slowly growing solutions


Authors: Janne Gröhn, Juha-Matti Huusko and Jouni Rättyä
Journal: Trans. Amer. Math. Soc. 370 (2018), 7201-7227
MSC (2010): Primary 30H10, 34M10
DOI: https://doi.org/10.1090/tran/7265
Published electronically: July 12, 2018
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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 $, $ \textup {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
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
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
Email: jouni.rattya@uef.fi

DOI: https://doi.org/10.1090/tran/7265
Keywords: Growth of solution, Hardy space, linear differential equation
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
Article copyright: © Copyright 2018 American Mathematical Society

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