Spectrum of a linear differential equation with constant coefficients

Abstract

In this paper we compute the spectrum, in the sense of Berkovich, of an ultrametric linear differential equation with constant coefficients, defined over an affinoid domain of the analytic affine line $A_k^{1,an}$. We show that it is a finite union of either closed disks or topological closures of open disks and that it satisfies a continuity property.