On Polynomially Bounded Harmonic Functions on the ${\bf Z}^d$ Lattice
Volume 57 / 2009
Bulletin Polish Acad. Sci. Math. 57 (2009), 231-242
MSC: Primary 31C05; Secondary 60G50.
DOI: 10.4064/ba57-3-5
Abstract
We prove that if $f:{\bf Z}^d \to {\bf R}$ is harmonic and there exists a polynomial $W:{\bf Z}^d \to {\bf R}$ such that $f+W$ is nonnegative, then $f$ is a polynomial.
