Abstract
This paper deals with a generalization of the classical Rarita-Schwinger equations for spin 3/2-fields to the case of functions taking values in irreducible representation spaces with weight k + 1/2 (realised as functions taking values in spaces of spherical monogenics earlier considered in [SVA2]). In this paper we consider such fields on smooth domains in ℝm.
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References
F. Brackx, R. Delanghe and F. Sommen: Clifford Analysis, Pitman, London, 1982.
J. Bures, F. Sommen, V. Soucek, P. Van Lancker: Rarita-Schwinger operators in Clifford Analysis, Preprint.
J. Bures, P. Van Lancker, F. Sommen, V. Souček: Symmetric analogues of Rarita-Schwing er equations, Preprint.
D. M. J. Calderbank: Clifford analysis for Dirac operators on manifolds with boundary, Report MPI 96–131.
R. Delanghe, F. Sommen, V. Soucek: Clifford analysis and spinor valued functions, Kluwer Acad. Publ., Dordrecht, 1992.
J. Gilbert and M. Murray: Clifford algebras and Dirac operators in harmonic analysis, Cambridge University Press, 1991.
N. Kerzman, E. M. Stein: The Cauchy kernel, the Szegö kernel, and the Riemann mapping function, Math. Ann. 236, 1978, pp. 85–93.
F. Sommen: Clifford analysis in two and several vector variables, Appl. Anal. Vol. 73(1-2), pp. 225–253.
V. Soucek: Higher Spins and Conformal Invariance in Clifford Analysis, Proc. Conf. Seiffen, 1996.
F. Sommen, N. Van Acker: Monogenic Differential Operators, Results in Math. 22, 1992, pp. 781–798.
F. Sommen, N. Van Acker: Invariant differential operators on polynomial valued functions, F. Brackx et al. (eds.), Clifford Algebras and their Applications in Mathematical Physics, Kluwer Acad. Publ., 1993, pp. 203–212.
P. Van Lancker: Clifford Analysis on the Unit Sphere, Ph. D. thesis, University of Gent, 1996.
P. Van Lancker: The Kerzman-Stein Theorem on the Sphere, to appear in Complex Variables.
P. Van Lancker, F. Sommen, D. Constales: Models for irreducible representations of Spin(m), to appear in the Proc. of Conf. on Dirac Operators, Cetraro, 1998.
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Van Lancker, P. (2001). Higher Spin Fields on Smooth Domains. In: Brackx, F., Chisholm, J.S.R., Souček, V. (eds) Clifford Analysis and Its Applications. NATO Science Series, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0862-4_33
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DOI: https://doi.org/10.1007/978-94-010-0862-4_33
Publisher Name: Springer, Dordrecht
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