Bohr–Rogosinski phenomenon for analytic functions and Cesáro operators

By Ilgiz R. Kayumov, D. Khammatova, Saminathan Ponnusamy. 2021

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Abstract There are a number of articles which deal with Bohr's phenomenon whereas only a few papers appeared in the literature on Rogosinski's radii for analytic functions defined on the unit disk | z | 1 . In this article, we introduce and investigate Bohr-Rogosinski's phenomenon for analytic functions defined for | z | 1 in a general setting. In addition we discuss and derive Bohr-Rogosinski's radii for Cesaro operators on the space of bounded analytic functions. Finally, we also obtain the Bohr-Rogosinski's radius for a class of subordinations. All the results are proved to be sharp.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8f9d5ec6b57ed5ba0196f4f57d30e0a9bc9ecd49