Analytic Functional Calculus in Quaternionic Framework

2019/02/11 by Florian-Horia Vasilescu, Vasilescu, Florian-Horia
Computer Science · Mathematics · #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1902.03850

openalex publication_date 2019/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Regarding quaternions as normal matrices, we first characterize the 2× 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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