Remote Access Transactions of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9947-1975-0379879-8
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

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