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Journal of Convex Analysis 26 (2019), No. 1, 117--127
Copyright Heldermann Verlag 2019

Zero Free Inner Function On Every Single Slice

Piotr Kot
Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland

We present a completely new construction of a holomorphic function whose real part has given radial limits a.e. on every slice. As an application, we obtain a holomorphic function which is inner on every slice.

Keywords: Holomorphic function, inner function.

MSC: 32E30, 32E35

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