Holomorphic Factorization of Matrices of Polynomials
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.
KeywordsHomogeneous Polynomial Bergman Kernel Principal Symbol Bergman Projection Proper Holomorphic Mapping
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- [CD3].David W. Catlin and John P. D’Angelo, An isometric embedding theorem for holomorphic bundles. (preprint)Google Scholar
- [D].John P. D’Angelo, Several complex variables and the geometry of real hypersurf aces, CRC Press, Boca Raton (1993).Google Scholar
- [F].Gerald B. Folland, Introduction to Partial Differential Equations, Princeton University Press (1976).Google Scholar