Polynomial solutions of quasi-homogeneous partial differential equations

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作者：

LUO Xuebo ZHENG Zhujun Institute of Applied Mathematics Northwestern Polytechnical University Xian China ^{[710072
]}

Institute of Mathematics Henan University Kaifeng China ^{[475001
]}

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Science in China,Ser.A. | 2001年 / Ser.A.2001卷 / 09期

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摘要：

<正>By means of a method of analytic number theory the following theorem is proved. Let p be a quasi-homogeneous linear partial differential operator with degree m, m > 0, w.r.ta dilation{δτ}τ<0 given by ( a1, …, an). Assume that either a1, …,an are positive rational numbers or m =ajaj for some a = (a1,…,an)∈In+. Then the dimension of the space of polynomial solutions of the equation p[u] =0 on Rn must be infinite.

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页数：8

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