Opuscula Mathematica
Opuscula Math. 35, no. 5 (), 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.
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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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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