Curvature invariant and generalized canonical operator models - II

TL;DR

This paper extends the study of quotient Hilbert modules in the Cowen-Douglas class from one variable to multiple variables, providing new similarity and isomorphism results for higher multiplicity cases.

Contribution

It generalizes previous single-variable results to multivariable settings and establishes new criteria for similarity and isomorphism of these modules.

Findings

Extended quotient Hilbert modules to multivariable case

Derived similarity and isomorphism conditions

Enhanced understanding of module structures in higher dimensions

Abstract

In [11] the authors investigated a family of quotient Hilbert modules in the Cowen-Douglas class over the unit disk constructed from classical Hilbert modules such as the Hardy and Bergman modules. In this paper we extend the results to the multivariable case of higher multiplicity. Moreover, similarity as well as isomorphism results are obtained.