Abstract
In this paper we construct a class of homogeneous Hilbert modules over the disc algebra \( \mathcal{A}(\mathbb{D}) \) as quotients of certain natural modules over the function algebra \( \mathcal{A}(\mathbb{D}^2 ) \). These quotient modules are described using the jet construction for Hilbert modules. We show that the quotient modules obtained this way, belong to the class Bk(\( \mathbb{D} \)) and that they are mutually inequivalent, irreducible and homogeneous.
The research of the first author was supported in part by a grant from the DST-NSF Science and Technology Cooperation Programme. The second author was supported by the Indian Statistical Institute.
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Misra, G., Roy, S.S. (2007). On the Irreducibility of a Class of Homogeneous Operators. In: Alpay, D., Vinnikov, V. (eds) System Theory, the Schur Algorithm and Multidimensional Analysis. Operator Theory: Advances and Applications, vol 176. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8137-0_3
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DOI: https://doi.org/10.1007/978-3-7643-8137-0_3
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