THE SPECTRAL PICTURE OF REINHARDT MEASURES

Using a combination of techniques from the theory of groupoids, the th eory of several complex variables, and single and multivariable operat or theory, we describe in detail the spectral picture of the commuting pair (M(z1), M(z2)) of multi plication operators by the coordinate fu nctions z(1) and z(2), acting on the Hilbert space P-2(mu) : = C[z(1), z(2)](-L2(mu)), for mu an arbitrary Reinhardt measure on C-2. (C) 199 5 Academic Press, Inc.