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envelope of holomorphy; integral formula; index; null-convexity; complex null cone; Lipschitz boundary
Analytic continuation and domains of holomorphy for solution to the complex Laplace and Dirac equations in $\bold C^n$ are studied. First, geometric description of envelopes of holomorphy over domains in $\bold E^n$ is given. In more general case, solutions can be continued by integral formulas using values on a real $n-1$ dimensional cycle in $\bold C^n$. Sufficient conditions for this being possible are formulated.
[1] Brackx F., Delanghe R., Sommen R.: Clifford Analysis. Research Notes in Mathematics No.76, Pitman 1982. Zbl 1058.30043
[2] Bureš M., Souček V.: Generalized hypercomplex analysis and its integral formulas. Complex Variables: Theory and Application 5 (1985), 53-70. MR 0822855
[3] Dodson M., Souček V.: Leray residues applied to the solution of the Laplace and Wave equations. Seminari di geometria, Bologna (1984), 93-107. MR 0866151
[4] Ryan J.: Cells of harmonicity and generalized Cauchy integral formula. Proc. London Math. Society (3) 60 (1990), 295-318. MR 1031455
[5] Siciak J.: Holomorphic continuation of harmonic functions. Ann. Polon. Math. 29 (1974), 67-73. MR 0352530 | Zbl 0247.32011
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