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arXiv · 1902.03850

Analytic Functional Calculus in Quaternionic Framework

Florian-Horia Vasilescu
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Abstract

Regarding quaternions as normal matrices, we first characterize the $2\times 2$ matrix-valued functions, defined on subsets of quaternions, whose values are quaternions. Then we investigate the regularity of quaternionic-valued functions, defined by the analytic functional calculus. Constructions of analytic functional calculi for real linear operators, in particular for quaternionic linear ones, are finally discussed, using a Riesz-Dunford-Gelfand type kernel in one variable, or a Martinelly type kernel in two variables.

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Florian-Horia Vasilescu. 2019-02-11. Analytic Functional Calculus in Quaternionic Framework. https://arxiv.org/abs/1902.03850

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