Martina \v Sim\accent 23unkov\'a
On Kelvin type transformation for Weinstein operator

Comment.Math.Univ.Carolinae 42,1 (2001) 99-109.

Abstract:The note develops results from [5] where an invariance under the M\"obius 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 $k\not =0$, $k\not =2$ no other transforms of this kind exist and for case $k=2$, all such transforms are described.

Keywords: harmonic morphisms, Kelvin transform, Weinstein operator
AMS Subject Classification: 31B05, 35J15, 35B05

PDF