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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 ⊆ ℂm is a bounded domain. LetM 0 ⊆M 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 =M ⊖M 0 The invariants are given explicitly in the particular case ofk = 2.

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Authors and Affiliations

  1. Texas A&M University, College Station, 77843, Texas, USA

    Ronald G. Douglas & Gadadhar Misra

  2. Indian Statistical Institute, R.V. College Post, 560 059, Bangalore, India

    Gadadhar Misra

Authors
  1. Ronald G. Douglas
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  2. Gadadhar Misra
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Correspondence to Ronald G. Douglas.

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Douglas, R.G., Misra, G. Equivalence of quotient Hilbert modules. Proc. Indian Acad. Sci. (Math. Sci.) 113, 281–291 (2003). https://doi.org/10.1007/BF02829607

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  • DOI: https://doi.org/10.1007/BF02829607

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