Higher order Pizzetti’s formulas

  • Grzegorz Łysik

    Jan Kochanowski University, Kielce, Poland


We introduce integral mean value functions which are averages of integral means over spheres/balls and over their images under the action of a discrete group of complex rotations. In the case of real analytic functions we derive higher order Pizzetti’s formulas. As applications we obtain a maximum principle for polyharmonic functions and a characterization of convergent solutions to higher order heat type equations.

Cite this article

Grzegorz Łysik, Higher order Pizzetti’s formulas. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 27 (2016), no. 1, pp. 105–115

DOI 10.4171/RLM/725