English

Analytic Functional Calculus in Quaternionic Framework

Functional Analysis 2019-02-12 v1

Abstract

Regarding quaternions as normal matrices, we first characterize the 2×22\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.

Keywords

Cite

@article{arxiv.1902.03850,
  title  = {Analytic Functional Calculus in Quaternionic Framework},
  author = {Florian-Horia Vasilescu},
  journal= {arXiv preprint arXiv:1902.03850},
  year   = {2019}
}