Public examination of a doctoral dissertation in the field of mathematics

Doctoral candidate: M.Sc. Janne Gröhn

Date and venue: 19.8.2011 at 12 noon, Metria, M103, Joensuu campus

**ABSTRACT**

This thesis introduces some recent findings concerning linear differential equations, where coefficient functions are analytic in the unit disc of the complex plane. A short comparison to the corresponding results in the complex plane is also given.

In this thesis a special attention is paid to the connection between the growth of coefficients and the growth of solutions in the case that coefficient functions belong either to weighted Bergman spaces or to weighted Hardy spaces. Some estimates for logarithmic derivatives, which are frequently useful in context of linear differential equations, are briefly discussed. This thesis contains also results on prescribed zeros of solutions of second order linear differential equations, where coefficient is analytic in the unit disc. Moreover, the connection between the coefficient and the Schwarzian derivative of a quotient of two linearly independent solutions of a second order linear differential equation is also further underscored.

The doctoral dissertation of M.Sc. Janne Gröhn entitled “*Results on complex differential equations in the unit disc” The opponent in the public examination is Professor James Langley, University of Nottingham, England and the custos is Professor Risto Korhonen of the University of Eastern Finland.* will be examined at the Faculty of Science and Forestry.

Photo available for download at http://www.uef.fi/vaitoskuvat

**Contact:** Janne Gröhn, tel. +358 44 563 9909, janne.grohn@uef.fi

Publishing year: 2011

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