Equivalence of quotient Hilbert modules

Abstract

Let M be a Hilbert module of holomorphic functions over a natural function algebra A(Ω), where Ω ⊆ C^m is a bounded domain. Let M₀ ⊆ M be the submodule of functions vanishing to orderk on a hypersurface Z ⊆ Ω. We describe a method, which in principle may be used, to construct a set of complete unitary invariants for quotient modules Q = M ⊖ M₀ The invariants are given explicitly in the particular case of k = 2.