``Newton polyhedra'' of distributions

B. Ya. Kazarnovskii

Izvestiya. Mathematics , Tome 68 (2004) no. 2, pp. 273-289.

Résumé

We consider systems of equations of the form $f_i(x)=0$, where the $f_i(x)$ are the Fourier transforms of distributions with fixed compact supports, and show that the average density of roots of such systems is determined by the geometry of the convex hulls of the supports of the distributions as their product in the ring of convex bodies.

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