| 拟齐次解析亚椭圆偏微分算子的一个必要条件 |
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| 引用本文： | 罗学波,马玉兰. 拟齐次解析亚椭圆偏微分算子的一个必要条件[J]. 系统科学与数学, 1999, 19(1): 024-028 |
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| 作者姓名： | 罗学波 马玉兰 |
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| 作者单位： | 西北工业大学数学所!西安，710072，太原重型机械学院!太原，030024 |
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| 摘 要： | 本文给出了拟齐次线性偏微分算子P（x,D）在原点为解析亚椭圆的一个必要条件：若u∈S，（Rn）；且Pu=0；则存在整函数v；Pv=0，v和u在x=0的某个邻域中重合
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| 关 键 词： | 拟齐次线性偏微分算子 解析亚椭圆性 实解析 |
A NECESSARY CONDITION FOR ANALYTIC HYPOELLIPTIC PSEUDO-HOMOGENEOUS PARTIAL DIFFERENTIAL OPERATORS |
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| Xue Bo LUO,Yu Lan MA. A NECESSARY CONDITION FOR ANALYTIC HYPOELLIPTIC PSEUDO-HOMOGENEOUS PARTIAL DIFFERENTIAL OPERATORS[J]. Journal of Systems Science and Mathematical Sciences, 1999, 19(1): 024-028 |
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| Authors: | Xue Bo LUO Yu Lan MA |
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| Affiliation: | (Institute of Machinery Institute, Taiyuan 030024) |
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| Abstract: | This paper gives a necessary condition for a linear partial differential operator P(x,D), which is homogeneous with respect to some dilations, to be analytic hypoelliptic at the origin as follows: Assume u implied by S'_(#mu#,#lambda#)(R~n)(for S'_(#mu#,#lambda#)R~n, see Introduction) and Pu=0. Then there exists an entire function v satisfying Pv=0 where v is consistent with u in some neighborhood of x=0. |
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| Keywords: | Pseudo-homogeneous linear partial differential operator analytic-hypoellipticity real analysis |
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