# 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

## Access Full Article

top## Abstract

top## How to cite

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
- Bureš M., Souček V., Generalized hypercomplex analysis and its integral formulas, Complex Variables: Theory and Application 5 (1985), 53-70. (1985) MR0822855
- 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

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.