| Title:
|
Envelopes of holomorphy for solutions of the Laplace and Dirac equations (English) |
| Author:
|
Kolář, Martin |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
3 |
| Year:
|
1991 |
| Pages:
|
479-494 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
envelope of holomorphy |
| Keyword:
|
integral formula |
| Keyword:
|
index |
| Keyword:
|
null-convexity |
| Keyword:
|
complex null cone |
| Keyword:
|
Lipschitz boundary |
| MSC:
|
15A66 |
| MSC:
|
30G35 |
| MSC:
|
32D10 |
| MSC:
|
35B60 |
| MSC:
|
35J05 |
| MSC:
|
35Q40 |
| idZBL:
|
Zbl 0759.32008 |
| idMR:
|
MR1159796 |
| . |
| Date available:
|
2009-01-08T17:46:25Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118429 |
| . |
| Reference:
|
[1] Brackx F., Delanghe R., Sommen R.: Clifford Analysis.Research Notes in Mathematics No.76, Pitman 1982. Zbl 1058.30043 |
| Reference:
|
[2] Bureš M., Souček V.: Generalized hypercomplex analysis and its integral formulas.Complex Variables: Theory and Application 5 (1985), 53-70. MR 0822855 |
| Reference:
|
[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 |
| Reference:
|
[4] Ryan J.: Cells of harmonicity and generalized Cauchy integral formula.Proc. London Math. Society (3) 60 (1990), 295-318. MR 1031455 |
| Reference:
|
[5] Siciak J.: Holomorphic continuation of harmonic functions.Ann. Polon. Math. 29 (1974), 67-73. Zbl 0247.32011, MR 0352530 |
| . |
