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Integral Equations and Operator Theory

, Volume 63, Issue 4, pp 595–599 | Cite as

A Classification of Homogeneous Operators in the Cowen-Douglas Class

  • Adam Korányi
  • Gadadhar MisraEmail author
Article

Abstract.

A complete list of homogeneous operators in the Cowen-Douglas class \(B_n({\mathbb{D}})\) is given. This classification is obtained from an explicit realization of all the homogeneous Hermitian holomorphic vector bundles on the unit disc under the action of the universal covering group of the bi-holomorphic automorphism group of the unit disc.

Mathematics Subject Classification (2000).

Primary 47B32 Secondary 14F05, 53B35 

Keywords.

Hermitizable Cowen-Douglas class reproducing kernel homogeneous holomorphic Hermitian vector bundle 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Lehman CollegeThe City University of New YorkBronxUSA
  2. 2.Department of MathematicsIndian Institute of ScienceBangaloreIndia

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