Details:
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 $P_1,\\\\dots, P_{i1}$. 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  02781077 
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Language  English  Journal  Complex Var. Theory Appl.  Volume  50  Number  6  Pages  389400  Year  2005  Edition  0  Translation 
No  Refereed 
No 
