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Let L be a semi-elliptic linear differential operator of second order with infinitely differentiable coefficients on an open set X of n-dimensional Euclidean space. Various properties of L will be discussed: L is hypoelliptic, L is of Hoermander type, L is nuclear, L generates a harmonic space on X.For background and an introduction to the subject:
J.Bliedtner-W.Hansen: Potential Theory - An Analytic and Probabilistic Approach to Balayage, Springer 1986