| s型加性算子与a型加性算子 |
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| 引用本文： | 颜心力.s型加性算子与a型加性算子[J].数学研究及应用,1984,4(2):15-19. |
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| 作者姓名： | 颜心力 |
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| 作者单位： | 西安冶金建筑学院 |
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| 摘 要： | 设有定义于某线性空间而取值于规定了乘法的另一线性空间的映象A,满足 A(x+y)=B_1(y)A_x+B_2(x)AY+C(x,y), 则A称为泛义加性算子。本文所研究的s型加性算子与α型加性算子是泛义加性算子的特例。它们分别是通常加性算子与E.Hill等关于指数函数(算子)概念的拓广。但引入方式与结论不同。
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| 收稿时间： | 1981/4/27 0:00:00 |
On the Additive Operators of type s and type a |
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| Yan Xinli.On the Additive Operators of type s and type a[J].Journal of Mathematical Research with Applications,1984,4(2):15-19. |
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| Authors: | Yan Xinli |
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| Institution: | Xi''an Institute of Metallurgical Architecture |
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| Abstract: | In theis paper, we introduce the concepts mentioned in the title. We have De Moivre's formula corresponding to the additive operator of type s. Boundedness, continuity and Frechet differentiability have been discussed. The necessary and sufficient conditions for the periodicity of the operators introduced are given. Two orthonormal (in the extended sense) systems of operators are obtained. The relation between the two types of operators is investigated and then Euler's formula and other new related formula are obtained. |
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