| 拟微分算子与正则余弦函数 |
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| 引用本文： | 张寄洲,郑权.拟微分算子与正则余弦函数[J].数学学报,1998,41(4):767-772. |
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| 作者姓名： | 张寄洲 郑权 |
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| 作者单位： | 武汉大学数学科学学院(张寄洲)，华中理工大学数学系(郑权) |
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| 基金项目： | 国家自然科学基金,霍英东教育基金 |
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| 摘 要： | 设Ｏｐｐ（ｆ）是Ｌｐ（Ｒｎ）（１ｐ＜∞）中具有象征ｆ∈Ｓｍρ，０的常系数拟微分算子．本文证明了在适当条件下，Ｏｐｐ（ｆ）在Ｌｐ（Ｒｎ）（１ｐ＜∞）中生成一个正则余弦函数，并将所得结果应用到对应的非齐次二阶Ｃａｕｃｈｙ问题．
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| 关 键 词： | 拟微分算子，正则余弦函数，Cauchy问题 |
Pseudodifferential Operators and Regularized Cosine Functions |
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| Zhang Jizhou.Pseudodifferential Operators and Regularized Cosine Functions[J].Acta Mathematica Sinica,1998,41(4):767-772. |
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| Authors: | Zhang Jizhou |
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| Institution: | Zhang Jizhou (Faculty of Mathematics Science, Wuhan University, Wuhan 430072, China) (Fax: 027-86835129, Email:zhangjz@hubu.edu.cn) Zheng Quan (Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China) (Fax: |
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| Abstract: | Let Op p(f) be the L p-realization of a pseudodifferential operator Op(f) with symbol f∈ S m ρ,0 having constant coefficients. We prove that Op p(f) on L p(R n) for 1p< ∞ generates a regularized cosine function under the suitable conditions on f(ζ). These results can be applied to the corresponding inhomogeneous second order Cauchy problems. |
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| Keywords: | Pseudodifferential operators Regularized cosine function Cauchy problem |
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