A classification of homogeneous operators in the Cowen-Douglas class

作者：Koranyi Adam; Misra Gadadhar^*

来源：Advances in Mathematics, 2011, 226(6): 5338-5360.

DOI：10.1016/j.aim.2011.01.012

• Hermitizable
• Cowen-Douglas class
• Reproducing kernel
• Homogeneous holomorphic Hermitian vector bundles

An explicit construction of all the homogeneous holomorphic Hermitian vector bundles over the unit disc D is given. It is shown that every such vector bundle is a direct sum of irreducible ones. Among these irreducible homogeneous holomorphic Hermitian vector bundles over D, the ones corresponding to operators in the Cowen-Douglas class B-n(D) are identified. The classification of homogeneous operators in B-n(D) is completed using an explicit realization of these operators. We also show how the homogeneous operators in B-n(D) split into similarity classes.

• 出版日期2011-4-1