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1 October 2015 Harmonic functions on the lattice: Absolute monotonicity and propagation of smallness
Gabor Lippner, Dan Mangoubi
Duke Math. J. 164(13): 2577-2595 (1 October 2015). DOI: 10.1215/00127094-3164790

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.

Citation

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Gabor Lippner. Dan Mangoubi. "Harmonic functions on the lattice: Absolute monotonicity and propagation of smallness." Duke Math. J. 164 (13) 2577 - 2595, 1 October 2015. https://doi.org/10.1215/00127094-3164790

Information

Received: 12 January 2014; Revised: 11 October 2014; Published: 1 October 2015
First available in Project Euclid: 5 October 2015

zbMATH: 1337.31015
MathSciNet: MR3405594
Digital Object Identifier: 10.1215/00127094-3164790

Subjects:
Primary: 31B05
Secondary: 35J05 , 60J10 , 65N22

Keywords: absolutely monotonic , Harmonic functions , three circles theorems

Rights: Copyright © 2015 Duke University Press

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Vol.164 • No. 13 • 1 October 2015
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