| Title:
|
On Kelvin type transformation for Weinstein operator (English) |
| Author:
|
Šimůnková, Martina |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
99-109 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator $W_k:=\Delta+\frac k{x_n}\frac{\partial}{\partial x_n}$ on $\Bbb R^n$ is proved. In this note there is shown that in the cases $k\neq 0$, $k\neq 2$ no other transforms of this kind exist and for case $k=2$, all such transforms are described. (English) |
| Keyword:
|
harmonic morphisms |
| Keyword:
|
Kelvin transform |
| Keyword:
|
Weinstein operator |
| MSC:
|
31B05 |
| MSC:
|
35B05 |
| MSC:
|
35J15 |
| idZBL:
|
Zbl 1115.31002 |
| idMR:
|
MR1825375 |
| . |
| Date available:
|
2009-01-08T19:08:38Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119226 |
| . |
| Reference:
|
[1] Kellogg O.D.: Foundation of Potential Theory.Springer-Verlag, Berlin, 1929 (reissued 1967). MR 0222317 |
| Reference:
|
[2] Leutwiler H.: On the Appell transformation.in: Potential Theory (ed. J. Král et al.), Plenum Press, New York, 1987, pp.215-222. Zbl 0685.35006, MR 0986298 |
| Reference:
|
[3] Brzezina M.: Appell type transformation for the Kolmogorov type operator.Math. Nachr. 169 (1994), 59-67. MR 1292797 |
| Reference:
|
[4] Brzezina M., Šimůnková M.: On the harmonic morphism for the Kolmogorov type operators.in: Potential Theory - ICPT 94, Walter de Gruyter, Berlin, 1996, pp.341-357. MR 1404718 |
| Reference:
|
[5] Akin Ö., Leutwiler H.: On the invariance of the solutions of the Weinstein equation under Möbius transformations.in: Classical and Modern Potential Theory and Applications (ed. K. GowriSankaran et al.), Kluwer Academic Publishers, 1994, pp.19-29. Zbl 0869.31005, MR 1321603 |
| . |
