Bohr Theorems For Slice Regular Functions Over Octonions

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS（2021）

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摘要

In this paper, we mainly investigate two versions of the Bohr theorem for slice regular functions over the largest alternative division algebras of octonions O. To this end, we establish the coefficient estimates for self-maps of the unit ball of O and the Caratheodory class in this setting. As a further application of the coefficient estimate, the 1/2-covering theorem is also proven for slice regular functions with convex image.

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关键词

function of one hypercomplex variable, division algebras, Bohr theorem, covering theorem

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