Equivalence of quotient Hilbert modules |
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| Authors: | Douglas Ronald G Misra Gadadhar |
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| Institution: | (1) Texas A&M University, College Station, 77843 Texas, USA;(2) Indian Statistical Institute, R.V. College Post, 560 059 Bangalore, India |
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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
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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| Keywords: | Hilbert modules function algebra quotient module longitudinal and transversal curvature kernel function jet and angle |
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