Idan Perl: Harmonic functions and polynomials on discrete groups.

Előadó: Idan Perl

Cím: Harmonic functions and polynomials on discrete groups.

Absztrakt: Alexopoulos proved that on a finitely generated nilpotent group, the restriction of a harmonic function of polynomial growth to a torsion-free nilpotent subgroup of finite index is always a polynomial. We give a simpler, more direct proof for this result using a more elementary definition for polynomials. We also show that the Laplacian operator is onto, and calculate the precise dimension of the space of harmonic functions of given polynomial growth, refining previous results.