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

Abstract

In this work we establish a connection between two classical notions, unrelated so far: Harmonic functions on the one hand and absolutely monotonic functions on the other hand. We use this to prove convexity type and propagation of smallness results for harmonic functions on the lattice.

20 pages; revised according to referees' comments; new references; two theorems added; simplified proof; conjecture restated; title changed; more friendly introduction

Cited by in corpus (2)

• On the sharpness of a three circles theorem for discrete harmonic functions
• Strong convexity for harmonic functions on compact symmetric spaces