Duke Mathematical Journal
- Duke Math. J.
- Volume 164, Number 13 (2015), 2577-2595.
Harmonic functions on the lattice: Absolute monotonicity and propagation of smallness
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.
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
Permanent link to this document
Digital Object Identifier
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]
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