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arXiv · math/0310263

Equivalence of quotient Hilbert modules

Ronald G. Douglas·Gadadhar Misra
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Abstract

Let $\cl{M}$ be a Hilbert module of holomorphic functions over a natural function algebra $\mathcal{A}(Ω)$, where $Ω\subseteq \bb{C}^m$ is a bounded domain. Let $\cl{M}_0\subseteq \cl{M}$ be the submodule of functions vanishing to order $k$ on a hypersurface $\cl{Z} \subseteq Ω$. We describe a method, which in principle may be used, to construct a set of complete unitary invariants for quotient modules $\cl{Q}=\cl{M} \ominus \cl{M}_0$. The invariants are given explicitly in the particular case of $k = 2$.

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Ronald G. Douglas, Gadadhar Misra. 2003-10-17. Equivalence of quotient Hilbert modules. https://arxiv.org/abs/math/0310263

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