Geodesic
On the Action of the Complex Monge--Amp\`ere Operator on Piecewise Linear Functions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 1, pp. 19-29

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The action of the mixed complex Monge–Ampère operator $(h_1,\cdots,h_k)\mapsto dd^ch_1\wedge\cdots\wedge dd^ch_k$ on piecewise linear functions $h_i$ is considered. The language of Monge–Ampère operators is used to transfer results on mixed volumes and tropical varieties to a broader context, which arises under the passage from polynomials to exponential sums. In particular, it is proved that the value of the Monge–Ampère operator depends only on the product of the functions $h_i$.
Keywords: Newton polytope, mixed volume, Monge–Ampère operator, exponential sum, tropical variety.
Mots-clés : pseudovolume 
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     author = {B. Ya. Kazarnovskii},
     title = {On the {Action} of the {Complex} {Monge--Amp\`ere} {Operator} on {Piecewise} {Linear} {Functions}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2014_48_1_a1/}
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B. Ya. Kazarnovskii. On the Action of the Complex Monge--Amp\`ere Operator on Piecewise Linear Functions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 1, pp. 19-29. http://geodesic.mathdoc.fr/item/FAA_2014_48_1_a1/