Abstract

Let G be a linear connected semisimple Lie group. We denote by U(g)^K the algebra of left invariant differential operators on G that are also right invariant by K, and Z(U(g)^K) denotes center of U(g)^K.

In this paper we give a suficient condition for a differential operator P in Z(U(g)^K) to have a fundamental solution on G. This result extends the same one obtained previously for real rank one Lie groups and groups with only one conjugacy class of Cartan subgroups.

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