Abstract
In this note some integral formulae for complex left regular mappings and for solutions of the complex Laplace equation are presented.These integral formulae are of two types (elliptic and hyperbolic) and there is a general procedure (described by V.Souček and M. Dodson for the Laplace equation in [3]) to transform one type into another, namely the Leray residue formula.In this way it is possible to derive from integral formulae in Clifford analysis e.g.Riesz’ integral formula for the solution of the wave equation in the Minkowski space and Penrose’s integral formula for a spin-1/2 massless field. There are good hopes that the new integral formula of hyperbolic type can be used to give further information on left regular mappings and spinor fields.
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References
J. Bures: ‘Some integral formulas in complex Clifford analysis’, Proc. 11th Winter School, Srni Suppl.Rend.Circolo Mat. Palermo, II,3, 1984, 81–87
J. Bureš: ‘A comparison of integral formulae of hyperbolic and elliptic type’, Proc. Conf.Diff.Geom. and its Appl. Nové Mésto 1983, II, 35–40.
M. Dodson, V. Souček:‘Leray residue applied to solutions of the Laplace and wave equations’, to appear in Seminarii di geometria, Bologna.
J. Ryan: ‘Complexified Clifford analysis’, Complex variables. 1, 1983, 115–149.
J. Bureš, V. Souček: ‘Generalized hypercomplex analysis and its integral formulae’, Complex variables, 5, 1985, 53–70
M. Riesz: ‘A geometric solution of the wave equation in space-time of even dimension’, Comm.Pure Appl. Math. XIII,19, 1960, 329–351
K. Imaeda:‘A new formulation of electromagnetism’, Nuovo Cimento 32B, 1976, 138–162
V. Souček:‘Complex-quaternionic analysis applied to spin-1/2 massless field’, Complex variables, 1, 1983, 327–346
L. Hörmander: The analysis of linear partial differential operators I. II. GMW 257, Springer Verlag, Berlin 1983
R. Penrose: ‘Null hypersurface initial data for classical fields of arbitrary spin and for general relativity’, Gen. Rel. and Gray. 12 No. 3, 1980, 225–264.
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© 1986 D. Reidel Publishing Company
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Bureš, J. (1986). Integral Formulae in Complex Clifford Analysis. In: Chisholm, J.S.R., Common, A.K. (eds) Clifford Algebras and Their Applications in Mathematical Physics. NATO ASI Series, vol 183. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4728-3_18
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DOI: https://doi.org/10.1007/978-94-009-4728-3_18
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