Harmonic functions on the lattice: Absolute monotonicity and propagation of smallness
Analysis of PDEs
2015-12-09 v3 Combinatorics
Probability
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.
Keywords
Cite
@article{arxiv.1312.4550,
title = {Harmonic functions on the lattice: Absolute monotonicity and propagation of smallness},
author = {Gabor Lippner and Dan Mangoubi},
journal= {arXiv preprint arXiv:1312.4550},
year = {2015}
}
Comments
20 pages; revised according to referees' comments; new references; two theorems added; simplified proof; conjecture restated; title changed; more friendly introduction