Publication
Title
The higher spin Laplace operator
Author
Abstract
This paper deals with a certain class of second-order conformally invariant operators acting on functions taking values in particular (finite-dimensional) irreducible representations of the orthogonal group. These operators can be seen as a generalisation of the Laplace operator to higher spin as well as a second-order analogue of the Rarita-Schwinger operator. To construct these operators, we will use the framework of Clifford analysis, a multivariate function theory in which arbitrary irreducible representations for the orthogonal group can be realised in terms of polynomials satisfying a system of differential equations. As a consequence, the functions on which this particular class of operators act are functions taking values in the space of harmonics homogeneous of degree k. We prove the ellipticity of these operators and use this to investigate their kernel, focusing on polynomial solutions. Finally, we will also construct the fundamental solution using the theory of Riesz potentials.
Language
English
Source (journal)
Potential analysis / Cranfield Campus. - London
Publication
London : 2017
ISSN
0926-2601
Volume/pages
47 :2 (2017) , p. 123-149
ISI
000405087700001
Full text (Publisher's DOI)
Full text (open access)
UAntwerpen
Faculty/Department
Research group
Project info
Construction of symmetry algebra realizations using Dirac operators.
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 02.08.2018
Last edited 20.09.2021
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