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 Title A surjectivity theorem for differential operators on spaces of regular functions Author(s) Fabrizio Colombo, Alberto Damiano, Irene Sabadini, Daniele C. Struppa Type Article in Journal Abstract Let $R$ be a commutative domain. An ordered set of square matrices $P_1,\\\\dots,P_k$ of size $n$ over $R$ is left regular if $P_1$ is not a right zero divisor in the algebra of these matrices and each $P_i$, $i\\\\geqslant 2$ is not a zero divisor modulo the right ideal generated by $P_1,\\\\dots, P_{i-1}$. For a regular sequence the authors find a set of generators of the first syzygy module and construct a classical Koszul complex. As a result it is shown that for any complex polynomial $p$ the operator $P(\\\\partial/\\\\partial q)$ is surjective on the space of regular functions and an operator of the form $\\\\partial^m/ \\\\partial_{x_1}^{m_1} \\\\partial_{x_2}^{m_2} \\\\partial_{x_3}^{m_3}$ on the space of regular functions on convex open sets in $\\\\Bbb H$. Keywords differential operators, Length 12 ISSN 0278-1077 File URL www.tlc185.com/coala Language English Journal Complex Var. Theory Appl. Volume 50 Number 6 Pages 389--400 Year 2005 Edition 0 Translation No Refereed No
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