Opuscula Math. 35, no. 5 (2015), 655-664
http://dx.doi.org/10.7494/OpMath.2015.35.5.655
Opuscula Mathematica
On mean-value properties for the Dunkl polyharmonic functions
Abstract. We derive differential relations between the Dunkl spherical and solid means of continuous functions. Next we use the relations to give inductive proofs of mean-value properties for the Dunkl polyharmonic functions and their converses.
Keywords: Dunkl Laplacian, Dunkl polyharmonic functions, mean-values, Pizzetti formula.
Mathematics Subject Classification: 31A30, 31B30, 33C52.
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- Grzegorz Łysik
- Polish Academy of Sciences, Institute of Mathematics, Śniadeckich 8, 00-656 Warsaw, Poland
- Jan Kochanowski University, Faculty of Mathematics and Natural Sciences, ul. Świętokrzyska 15, 25-406 Kielce, Poland
- Communicated by Semyon B. Yakubovich.
- Received: 2013-12-13.
- Revised: 2014-07-04.
- Accepted: 2014-07-08.
- Published online: 2015-04-27.
