Some Results on the Vanishing Conjecture of Differential Operators with Constant Coefficients
Some Results on the Vanishing Conjecture of Differential Operators with Constant Coefficients
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DOI：
10.1016/j.jpaa.2014.12.024
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发表时间：
2009-03
期刊：
影响因子：
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通讯作者：
A. Essen;Roel M. Willems;Wenhua Zhao
中科院分区：
文献类型：
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作者：
A. Essen;Roel M. Willems;Wenhua Zhao
本文证明了第三作者在[15]中提出的关于常系数微分算子的消失猜想的四种情形以及关于无全纯部分的Laurent多项式的一个猜想。本文还通过两个例子说明了消失猜想和Duistermaat-van der Kallen定理[6]不能推广到一般的（Laurent）形式幂级数的情形。
In this paper we prove four cases of theVanishing Conjectureof differential operators with constant coefficients and also a conjecture on the Laurent polynomials with no holomorphic parts, which were proposed in [15] by the third named author. We also give two examples to show that both theVanishing Conjectureand theDuistermaat–van der Kallen Theorem[6] cannot be generalized to the setting of (Laurent) formal power series in general.