On the sharpness of a three circles theorem for discrete harmonic functions

Abstract

Any three circles theorem for discrete harmonic functions must contain an inherent error term. In this paper we find the sharp error term in an $L^2$-three circles theorem for harmonic functions defined in $\Zb^2$. The proof is highly indirect due to combinatorial obstacles and cancellations phenomena. We exploit Newton interpolation methods and recursive arguments.

17 pages

References in corpus (1)

• Harmonic functions on the lattice: Absolute monotonicity and propagation of smallness