A dilation theory approach to cubature formulas. II

An interpretation of multivariate cubature formulas for positive measures i n terms of Hilbert space operators leads to a parametrization of all finite - rank, cyclic and commutative dilations of a given cyclic tuple of self-a djoint operators. Explicit matricial formulas for these dilations are prese nted; the abstract dilation problem suggested by the concrete computations is stated at the end of the note.