Linear differential equations with slowly growing solutions

Gröhn, Janne; Huusko, Juha-Matti; Rättyä, Jouni

doi:10.1090/tran/7265

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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