The $H^\infty$-functional calculi for the quaternionic fine structures of Dirac type
Abstract
In this paper, we utilize various integral representations derived from the Fueter-Sce extension theorem, to introduce novel functional calculi tailored for quaternionic operators of sectorial type. Specifically, due to the different factorizations of the Laplace opertor with respect to the Cauchy-Fueter operator and its conjugate, we identify four distinct classes of functions: Slice hyperholomorphic functions (leading to the -functional calculus), axially harmonic functions (leading to the -functional calculus), axially polyanalytic functions of order (leading to the -functional calculus), and axially monogenic functions (leading to the -functional calculus). By applying the respective product rule, we establish the four different -versions of these functional calculi.
Cite
@article{arxiv.2312.02064,
title = {The $H^\infty$-functional calculi for the quaternionic fine structures of Dirac type},
author = {Fabrizio Colombo and Stefano Pinton and Peter Schlosser},
journal= {arXiv preprint arXiv:2312.02064},
year = {2024}
}