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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Holomorphic functions with growth conditions
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by Bent E. Petersen PDF
Trans. Amer. Math. Soc. 206 (1975), 395-406 Request permission

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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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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