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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Holomorphic functions with growth conditions

Author: Bent E. Petersen
Journal: Trans. Amer. Math. Soc. 206 (1975), 395-406
MSC: Primary 32A10; Secondary 35E05
MathSciNet review: 0379879
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Abstract: Let $ P$ be a $ p \times q$ matrix of polynomials in $ n$ complex variables. If $ \Omega $ is a domain of holomorphy in $ {{\mathbf{C}}^n}$ and $ u$ is a $ q$-tuple of holomorphic functions we show that the equation $ Pv = Pu$ has a solution $ v$ which is a holomorphic $ q$-tuple in $ \Omega $ and which satisfies an $ {L^2}$ estimate in terms of $ Pu$. Similar results have been obtained by Y.-T. Siu and R. Narasimhan for bounded domains and by L. Höormander for the case $ \Omega = {{\mathbf{C}}^n}$.

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Keywords: Holomorphic functions, cohomology with bounds
Article copyright: © Copyright 1975 American Mathematical Society

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