| $W^m_2 [a,b]$ 空间中再生核的计算(Ⅰ) |
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| 引用本文： | 张新建,龙汉.$W^m_2 [a,b]$ 空间中再生核的计算(Ⅰ)[J].计算数学,2008,30(3):295-304. |
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| 作者姓名： | 张新建 龙汉 |
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| 作者单位： | 国防科技大学理学院数学系,长沙,410073 |
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| 摘 要： | 本文用Green函数与伴随函数方法讨论由一般线性微分算子确定的再生核的具体计算.提出了基本Green函数与基本再生核的概念,它们是由微分算子和初值点唯一确定的;指出基本再生核的计算可转化为求解微分方程的初值问题,一般的再生核可由基本再生核的投影而得到;最后用例子说明了所给方法.
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| 关 键 词： | Green函数 线性微分算子 基本再生核 再生核 投影 |
COMPUTING REPRODUCING KERNELS FOR Wm2[a,b](Ⅰ) |
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| Zhang Xinjian,Long Han.COMPUTING REPRODUCING KERNELS FOR Wm2[a,b](Ⅰ)[J].Mathematica Numerica Sinica,2008,30(3):295-304. |
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| Authors: | Zhang Xinjian Long Han |
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| Institution: | College of Science, National University of Defense and Technology, Changsha 410073, China |
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| Abstract: | In this paper, the adjunct and Green functions are used to develop a concrete method for computing the reproducing kernels for arbitrary linear differential operators. The basic Green function and the basic reproducing kernel are defined, make use of these, we prove that the problem of computing the basic kernel can be decomposed into some simpler initial value problems and a general reproducing kernel is the projection of the basic kernel. |
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