Let {Zj} be a finite collection of vector fields, with smooth complex-valued coefficients, defined in an open subset U of Euclidean space. Let Z∗ j be the formal adjoint of Zj , with respect to the Hilbert space structure L2 associated to some measure with a smooth nonvanishing density. Consider the operator L = ∑ j Z ∗ jZj, which we shall refer to as a sum of squares. L is said to be hypoellip...