GLOBAL HYPOELLIPTICITY OF A CLASS OF 2ND-ORDER OPERATORS

We show that almost all perturbations P - lambda, lambda is-an-element-of C, of an arbitrary constant coefficient partial differential operator P are globally hypoelliptic on the torus. We also give a characterization of the values lambda is-an-element-of C for which the operator D(t)2 - 2D(x)2 - lambda is globally hypoelliptic; in particular, we show that the addition of a term of order zero may destroy the property of global hypoellipticity of operators of principal type, contrary to that happens with the usual (local) hypoellipticity.