Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 32A10, 35E05

Retrieve articles in all journals with MSC: 32A10, 35E05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0379879-8
PII: S 0002-9947(1975)0379879-8
Keywords: Holomorphic functions, cohomology with bounds
Article copyright: © Copyright 1975 American Mathematical Society