Envelopes of holomorphy for solutions of the Laplace and Dirac equations
Commentationes Mathematicae Universitatis Carolinae (1991)
- Volume: 32, Issue: 3, page 479-494
- ISSN: 0010-2628
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topKolář, Martin. "Envelopes of holomorphy for solutions of the Laplace and Dirac equations." Commentationes Mathematicae Universitatis Carolinae 32.3 (1991): 479-494. <http://eudml.org/doc/247304>.
@article{Kolář1991,
abstract = {Analytic continuation and domains of holomorphy for solution to the complex Laplace and Dirac equations in $\mathbf \{C\}^n$ are studied. First, geometric description of envelopes of holomorphy over domains in $\mathbf \{E\}^n$ is given. In more general case, solutions can be continued by integral formulas using values on a real $n-1$ dimensional cycle in $\mathbf \{C\}^n$. Sufficient conditions for this being possible are formulated.},
author = {Kolář, Martin},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {envelope of holomorphy; integral formula; index; null-convexity; complex null cone; Lipschitz boundary; integral formula; complex Dirac equation; Laplace equation; envelope of holomorphy},
language = {eng},
number = {3},
pages = {479-494},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Envelopes of holomorphy for solutions of the Laplace and Dirac equations},
url = {http://eudml.org/doc/247304},
volume = {32},
year = {1991},
}
TY - JOUR
AU - Kolář, Martin
TI - Envelopes of holomorphy for solutions of the Laplace and Dirac equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 3
SP - 479
EP - 494
AB - Analytic continuation and domains of holomorphy for solution to the complex Laplace and Dirac equations in $\mathbf {C}^n$ are studied. First, geometric description of envelopes of holomorphy over domains in $\mathbf {E}^n$ is given. In more general case, solutions can be continued by integral formulas using values on a real $n-1$ dimensional cycle in $\mathbf {C}^n$. Sufficient conditions for this being possible are formulated.
LA - eng
KW - envelope of holomorphy; integral formula; index; null-convexity; complex null cone; Lipschitz boundary; integral formula; complex Dirac equation; Laplace equation; envelope of holomorphy
UR - http://eudml.org/doc/247304
ER -
References
top- Brackx F., Delanghe R., Sommen R., Clifford Analysis, Research Notes in Mathematics No.76, Pitman 1982. Zbl1058.30043
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- Dodson M., Souček V., Leray residues applied to the solution of the Laplace and Wave equations, Seminari di geometria, Bologna (1984), 93-107. (1984) MR0866151
- Ryan J., Cells of harmonicity and generalized Cauchy integral formula, Proc. London Math. Society (3) 60 (1990), 295-318. (1990) MR1031455
- Siciak J., Holomorphic continuation of harmonic functions, Ann. Polon. Math. 29 (1974), 67-73. (1974) Zbl0247.32011MR0352530
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