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

Gabor Lippner, Dan Mangoubi
2015 Duke mathematical journal  
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.
doi:10.1215/00127094-3164790 fatcat:doadw72e55erbaeajzvhuvufue