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BY 4.0 license Open Access Published by De Gruyter Open Access July 5, 2021

Spectrum and Analytic Functional Calculus for Clifford Operators via Stem Functions

  • Florian-Horia Vasilescu EMAIL logo
From the journal Concrete Operators

Abstract

The main purpose of this work is the construction of an analytic functional calculus for Clifford operators, which are operators acting on certain modules over Clifford algebras. Unlike in some preceding works by other authors, we use a spectrum defined in the complex plane, and also certain stem functions, analytic in neighborhoods of such a spectrum. The replacement of the slice regular functions, having values in a Clifford algebra, by analytic stem functions becomes possible because of an isomorphism induced by a Cauchy type transform, whose existence is proved in the first part of this work.

MSC 2010: 30G35; 30A05; 47A10; 47A60

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Received: 2021-01-25
Accepted: 2021-05-25
Published Online: 2021-07-05

© 2021 Florian-Horia Vasilescu, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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