On Kelvin type transformation for Weinstein operator

Martina Šimůnková

Commentationes Mathematicae Universitatis Carolinae (2001)

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

Abstract

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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 : = Δ + k x n ∂ ∂ x n on ℝ n is proved. In this note there is shown that in the cases k ≠ 0 , k ≠ 2 no other transforms of this kind exist and for case k = 2 , all such transforms are described.

How to cite

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Šimůnková, 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

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

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