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(2012)ANNALS OF GLOBAL ANALYSIS AND GEOMETRY.41(2).p.161-186 Mark abstract Spherical monogenics can be regarded as a basic tool for the study of harmonic analysis of the Dirac operator in Euclidean space R(m). They play a similar role as spherical harmonics do in case of harmonic analysis of the Laplace operator on Rm. Fix the direct sum R(m) = R(p) circle plus R(q). In this article, we will study the decomposition of the space M(n)(R(m), C(m)) of spherical monogenics of order n under the action of Spin(p) x Spin(q). As a result, we obtain a Spin(p) x Spin(q)- invariant orthonormal basis for M(n)(R(m), C(m)). In particular, using the construction with p = 2 inductively, this yields a new orthonormal basis for the space M(n)(R(m), C(m)).

Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-2154824

Author: Roman Lávička, Vladimir Souček and Peter Van Lancker

Source: https://biblio.ugent.be/publication/2154824


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