THE SPECTRAL PICTURE OF REINHARDT MEASURES

Using a combination of techniques from the theory of groupoids, the theory of several complex variables, and single and multivariable operator theory, we describe in detail the spectral picture of the commuting pair (M(z1), M(z2)) of multi plication operators by the coordinate functions 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) 1995 Academic Press, Inc.