Fractional powers of Clifford d-bar and radial derivatives

Abstract

We introduce new non-local derivative operators in the context of Clifford analysis, by giving meaning to fractional powers of the d-bar and radial derivatives in this setting. The definitions arise from binomial-type series constructions, and we justify them by proving natural properties including semigroup/composition properties and the new operators' action on special functions acting on paravectors. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.