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 (Mz1, Mz2) of multiplication operators by the coordinate functions z1 and z2, acting on the Hilbert space P2(μ) := C[z1, z2]−L2(μ), for μ an arbitrary Reinhardt measure on C2.