  These notes are inspired by the theory of cellular automata. A linear
cellular automaton on a lattice of finite rank or on a toric grid is a discrete
dinamical system generated by a convolution operator with kernel concentrated
in the nearest neighborhood of the origin. In the present paper we deal with
general convolution operators. We propose an approach via harmonic analysis
which works over a field of positive characteristic. It occurs that a standard
spectral problem for a convolution operator is equivalent to counting points on
an associate algebraic hypersurface in a torus according to the torsion orders
of their coordinates.
