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A Martinelli-Bochner formula for the Hermitian Dirac equation. (English) Zbl 1117.30040
In this paper, the authors present a generalization of the Martinelli-Bochner formula in several complex variables which is derived for a Hermitian Dirac operator.

MSC:
30G35 Functions of hypercomplex variables and generalized variables
30-XX Functions of a complex variable
32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
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[1] , . Clifford Analysis. Research Notes in Mathematics, vol. 76. Advanced Publishing Program, Pitman: Boston, 1982. · Zbl 0529.30001
[2] , . The Hermitian Clifford Analysis Toolbox. Submitted. · Zbl 1177.30064
[3] , . Integral Theorems for Functions and Differential Forms in \(\mathbb{C}\)m. Research Notes in Mathematics, vol. 428. Chapman & Hall/CRC: London, Boca Raton, FL, 2002.
[4] Sabadini, Mathematical Methods in the Applied Sciences 25 pp 1395– (2002)
[5] Brackx, Complex Variables Theory Application 4 pp 39– (1984)
[6] , . Clifford algebra and spinor-valued functions. Mathematics and its Applications, vol. 53. Kluwer Academic Publishers: Dordrecht, 1992.
[7] . Harmonic analysis for general first order differential operators in Lipschitz domains. Clifford Algebras. Cookeville, TN, 2002; 91–114;
[8] Progress in Mathematical Physics, vol. 34. Birkhäuser: Boston, MA, 2004.
[9] Martinelli, Annali di Matematica Pura ed Applicata 34 pp 277– (1953)
[10] Sommen, Zeitschrift fur Analysis und Ihre Anwendungen 6 pp 75– (1987)
[11] Sommen, Journal of Natural Geometry 24 pp 71– (2003)
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