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In this paper an integral transform between spaces of nonstandard testfunctions on the affine space of dimension n is constructed. The integraltransform satisfies a summation formula of Poisson type, which is derived froman analogue of the Arthur-Selberg trace formula for the Lie algebra of n by nmatrices.

A Global Trace Formula for Reductive Lie Algebras and the Harish-Chandra Transform on the Space of Characteristic Polynomials