Equivalence of quotient Hilbert modules -- II
Abstract
For any open, connected and bounded set , let be a natural function algebra consisting of functions holomorphic on . Let be a Hilbert module over the algebra and be the submodule of functions vanishing to order on a hypersurface . Recently the authors have obtained an explicit complete set of unitary invariants for the quotient module in the case of . 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.
Cite
@article{arxiv.math/0507553,
title = {Equivalence of quotient Hilbert modules -- II},
author = {Ronald G. Douglas and Gadadhar Misra},
journal= {arXiv preprint arXiv:math/0507553},
year = {2007}
}
Comments
The introduction has been revised and streamlined. The material has been reorganized slightly