Year: 2020
Type: preprint
Abstract: We present an approach to the spectrum and analytic functional calculus for quaternionic linear operators, following the corresponding results concerning the real linear operators. In fact, the construction of the analytic functional calculus for real linear operators can be refined to get a similar construction for quaternionic linear ones, in a classical manner, using a Riesz-Dunford-Gelfand type kernel, and considering spectra in the complex plane. A quaternionic joint spectrum for pairs of operators is also discussed, and an analytic functional calculus is constructed, via a Martinelli type kernel in two variables.
Source: arXiv (Cornell University)
Author: Vasilescu, Florian-Horia
Institution: Université de Lille
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3011081404