Eqivalence of quotient Hilbert modules - II

Douglas, Ronald G. ; Misra, Gadadhar (2008) Eqivalence of quotient Hilbert modules - II Transactions of the American Mathematical Society, 360 . pp. 2229-2264. ISSN 0002-9947

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Abstract

For any open, connected and bounded set Ω ⊆ Cm, let A be a natural function algebra consisting of functions holomorphic on Ω. Let M be a Hilbert module over the algebra A and M0 ⊆ M be the submodule of functions vanishing to order k on a hypersurface Z ⊆ Ω. Recently the authors have obtained an explicit complete set of unitary invariants for the quotient module Q = M⊝ M0 in the case of 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 homogeneous modules over the bi-disc algebra.

Item Type:Article
Source:Copyright of this article belongs to American Mathematical Society.
ID Code:66992
Deposited On:28 Oct 2011 10:31
Last Modified:18 May 2016 14:17

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