Abstract:
The action of the mixed complex Monge–Ampère operator (h1,⋯,hk)↦ddch1∧⋯∧ddchk(h1,⋯,hk)↦ddch1∧⋯∧ddchk on piecewise linear functions hihi 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 hihi.
Citation:
B. Ya. Kazarnovskii, “On the Action of the Complex Monge–Ampère Operator on Piecewise Linear Functions”, Funktsional. Anal. i Prilozhen., 48:1 (2014), 19–29; Funct. Anal. Appl., 48:1 (2014), 15–23
\Bibitem{Kaz14}
\by B.~Ya.~Kazarnovskii
\paper On the Action of the Complex Monge--Amp\`ere Operator on Piecewise Linear Functions
\jour Funktsional. Anal. i Prilozhen.
\yr 2014
\vol 48
\issue 1
\pages 19--29
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\jour Funct. Anal. Appl.
\yr 2014
\vol 48
\issue 1
\pages 15--23
\crossref{https://doi.org/10.1007/s10688-014-0042-3}
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Linking options:
https://www.mathnet.ru/eng/faa3125
https://doi.org/10.4213/faa3125
https://www.mathnet.ru/eng/faa/v48/i1/p19
This publication is cited in the following 7 articles:
B. Ya. Kazarnovskii, “Ob eksponentsialnoi algebraicheskoi geometrii”, UMN, 80:1(481) (2025), 3–58
B. Ya. Kazarnovskii, “Distribution of zeros of functions with exponential growth”, Sb. Math., 215:3 (2024), 355–363
Francesco Paolo Gallinaro, “Exponential sums equations and tropical geometry”, Sel. Math. New Ser., 29:4 (2023)
B. Ya. Kazarnovskii, “The quasi-algebraic ring of conditions of $\mathbb C^n$”, Izv. Math., 86:1 (2022), 169–202
B. Ya. Kazarnovskii, A. G. Khovanskii, A. I. Esterov, “Newton polytopes and tropical geometry”, Russian Math. Surveys, 76:1 (2021), 91–175
B. Ya. Kazarnovskii, “On the product of cocycles in a polyhedral complex”, Izv. Math., 81:2 (2017), 329–358
B. Ya. Kazarnovskii, “Action of the complex Monge–Ampère operator on piecewise-linear functions and exponential tropical varieties”, Izv. Math., 78:5 (2014), 902–921
Citation in format AMSBIB
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