Opuscula Math. 35, no. 5 (2015), 655-664

Opuscula Mathematica

On mean-value properties for the Dunkl polyharmonic functions

Grzegorz Łysik

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
  • Received: 2013-12-13.
  • Revised: 2014-07-04.
  • Accepted: 2014-07-08.
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Cite this article as:
Grzegorz Łysik, On mean-value properties for the Dunkl polyharmonic functions, Opuscula Math. 35, no. 5 (2015), 655-664, http://dx.doi.org/10.7494/OpMath.2015.35.5.655

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