Equivalence of quotient Hilbert modules-II |
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Authors: | Ronald G Douglas Gadadhar Misra |
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Institution: | Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368 ; Statistics and Mathematics Unit, Indian Statistical Institute, R. V. College Post, Bangalore 560 059, India |
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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 let 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. |
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Keywords: | Hilbert modules complex geometry jet bundles curvature homogeneous operators |
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