Duke Mathematical Journal

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

Gabor Lippner and Dan Mangoubi

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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.

Article information

Duke Math. J. Volume 164, Number 13 (2015), 2577-2595.

Received: 12 January 2014
Revised: 11 October 2014
First available in Project Euclid: 5 October 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 31B05: Harmonic, subharmonic, superharmonic functions
Secondary: 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx] 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 65N22: Solution of discretized equations [See also 65Fxx, 65Hxx]

harmonic functions absolutely monotonic three circles theorems


Lippner, Gabor; Mangoubi, Dan. Harmonic functions on the lattice: Absolute monotonicity and propagation of smallness. Duke Math. J. 164 (2015), no. 13, 2577--2595. doi:10.1215/00127094-3164790. https://projecteuclid.org/euclid.dmj/1444051069

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