Introduction. Let D = Gammaid=dx denote the unbounded operator of differentiation in L 2 (R), and let M denote the unbounded operator in L 2 (R) of multiplication by the function ¸(x) = x. Then D and M are selfadjoint, non-commuting operators. The problem of how to form "functions" of the pair (D; M) is an old and imprecise one in that the non-commutativity of D and M allows for more than one functional calculus for the pair (D; M ); see [4] and [7], for example. For instance, the Kohn-Nirenberg calculus is specified by the formula f KN (D; M) = (2ß) Gamma1 Z R 2 e i¸ 1<F47.22