Moment vanishing problem and positivity: Some examples
Moment vanishing problem and positivity: Some examples
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DOI：
10.1016/j.bulsci.2010.06.002
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发表时间：
2011
影响因子：
1.3
通讯作者：
J. Françoise;F. Pakovich;Y. Yomdin;Wenhua Zhao
中科院分区：
文献类型：
--
作者：
J. Françoise;F. Pakovich;Y. Yomdin;Wenhua Zhao
我们考虑Ω的矩的零化问题是Rnand P(X)，Q(X)复多项式在x∈Ω(Mvp)中的紧域。主要强调这一一般的消失问题与最近在Mathieu(1997)[22]，Duistermaat和van der Kallen(1998)[17]，赵(2010)[34，35]和其他出版物中研究的下列猜想之间的关系，这些猜想与微分算子的消失问题和Jacobian猜想有关：我们回顾了Muzychuk和Pakovich(2009)[24]，Pakovich(2009,2004)[25，26]，Pakovich(预印本)[28]中关于一维(MVP)的最新结果，并证明了一些初步结果强调了正性假设在度量μ中的作用。在此基础上，我们分析了猜想A的一些特殊情况，并在这些情况下给出了猜想成立的测度μ的完整刻画。
We consider the problem of vanishing of the moments with Ω a compact domain in Rnand P(x), q(x) complex polynomials in x∈Ω (MVP). The main stress is on relations of this general vanishing problem to the following conjecture which has been studied recently in Mathieu (1997) [22], Duistermaat and van der Kallen (1998) [17], Zhao (2010) [34,35] and in other publications in connection with the vanishing problem for differential operators and with the Jacobian conjecture: We recall recent results on one-dimensional (MVP) obtained in Muzychuk and Pakovich (2009) [24], Pakovich (2009,2004) [25,26], Pakovich (preprint) [28] and prove some initial results in several variables, stressing the role of the positivity assumption on the measure μ. On this base we analyze some special cases of Conjecture A and provide in these cases a complete characterization of the measures μ for which this conjecture holds.