Equivalence of quotient Hilbert modules–II

Author:

Douglas Ronald,Misra Gadadhar

Abstract

For any open, connected and bounded set Ω C m \Omega \subseteq \mathbb {C}^m , let A \mathcal A be a natural function algebra consisting of functions holomorphic on Ω \Omega . Let M \mathcal M be a Hilbert module over the algebra A \mathcal A and let M 0 M \mathcal M_0\subseteq \mathcal M be the submodule of functions vanishing to order k k on a hypersurface Z Ω \mathcal Z \subseteq \Omega . Recently the authors have obtained an explicit complete set of unitary invariants for the quotient module Q = M M 0 \mathcal Q=\mathcal M \ominus \mathcal M_0 in the case of k = 2 k=2 . In this paper, we relate these invariants to familiar notions from complex geometry. We also find a complete set of unitary invariants for the general case. We discuss many concrete examples in this setting. As an application of our equivalence results, we characterise certain homogeneous Hilbert modules over the bi-disc algebra.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference28 articles.

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