Equivalence of quotient Hilbert modules

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Abstract

LetM be a Hilbert module of holomorphic functions over a natural function algebraA(Ω), where Ω ⊆ ℂ m is a bounded domain. LetM 0M be the submodule of functions vanishing to orderk on a hypersurfaceZ ⊆ Ω. We describe a method, which in principle may be used, to construct a set of complete unitary invariants for quotient modulesQ =MM 0 The invariants are given explicitly in the particular case ofk = 2.