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arXiv · 1312.4550

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

Gabor Lippner·Dan Mangoubi
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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.

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Gabor Lippner, Dan Mangoubi. 2013-12-16. Harmonic functions on the lattice: Absolute monotonicity and propagation of smallness. https://doi.org/10.1215/00127094-3164790

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