# On Kelvin type transformation for Weinstein operator

Commentationes Mathematicae Universitatis Carolinae (2001)

- Volume: 42, Issue: 1, page 99-109
- ISSN: 0010-2628

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topŠimůnková, Martina. "On Kelvin type transformation for Weinstein operator." Commentationes Mathematicae Universitatis Carolinae 42.1 (2001): 99-109. <http://eudml.org/doc/248814>.

@article{Šimůnková2001,

abstract = {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 $\mathbb \{R\}^n$ is proved. In this note there is shown that in the cases $k\ne 0$, $k\ne 2$ no other transforms of this kind exist and for case $k=2$, all such transforms are described.},

author = {Šimůnková, Martina},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {harmonic morphisms; Kelvin transform; Weinstein operator; harmonic morphisms; Kelvin transform; Weinstein operator},

language = {eng},

number = {1},

pages = {99-109},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {On Kelvin type transformation for Weinstein operator},

url = {http://eudml.org/doc/248814},

volume = {42},

year = {2001},

}

TY - JOUR

AU - Šimůnková, Martina

TI - On Kelvin type transformation for Weinstein operator

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2001

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 42

IS - 1

SP - 99

EP - 109

AB - 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 $\mathbb {R}^n$ is proved. In this note there is shown that in the cases $k\ne 0$, $k\ne 2$ no other transforms of this kind exist and for case $k=2$, all such transforms are described.

LA - eng

KW - harmonic morphisms; Kelvin transform; Weinstein operator; harmonic morphisms; Kelvin transform; Weinstein operator

UR - http://eudml.org/doc/248814

ER -

## References

top- Kellogg O.D., Foundation of Potential Theory, Springer-Verlag, Berlin, 1929 (reissued 1967). MR0222317
- Leutwiler H., On the Appell transformation, in: Potential Theory (ed. J. Král et al.), Plenum Press, New York, 1987, pp.215-222. Zbl0685.35006MR0986298
- Brzezina M., Appell type transformation for the Kolmogorov type operator, Math. Nachr. 169 (1994), 59-67. (1994) MR1292797
- 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. MR1404718
- 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. Zbl0869.31005MR1321603

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