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Holomorphic Factorization of Matrices of Polynomials

  • John P. D’Angelo
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 3)

Abstract

This paper considers some work done by the author and Catlin [CD1,CD2,CD3] concerning positivity conditions for bihomogeneous polynomials and metrics on bundles over certain complex manifolds. It presents a simpler proof of a special case of the main result in [CD3], providing also a self-contained proof of a generalization of the main result from [CD1]. Some new examples and applications appear here as well. The idea is to use the Bergman kernel function and some operator theory to prove purely algebraic theorems about matrices of polynomials.

Keywords

Homogeneous Polynomial Bergman Kernel Principal Symbol Bergman Projection Proper Holomorphic Mapping 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • John P. D’Angelo
    • 1
  1. 1.Dept. of MathematicsUniversity of IllinoisUrbanaUSA

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