| 4n-2阶发展方程的酉半群讨论 |
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| 引用本文： | 张利勋,刘永智,欧中华,代志勇,彭增寿.4n-2阶发展方程的酉半群讨论[J].电子科技大学学报（自然科学版）,2006,35(1):130-132. |
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| 作者姓名： | 张利勋 刘永智 欧中华 代志勇 彭增寿 |
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| 作者单位： | 1.电子科技大学光电信息学院 成都 610054 |
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| 摘 要： | 将4n-2阶发展方程转化为一阶发展方程组,求得4n-2阶发展方程的生成算子,在一定的条件下由E.Hille-E.Yosida定理生成半群。讨论了4n-2阶发展方程的生成算子生成的算子半群的酉性,研究表明:n>1时均要附加共轭算子范数相等条件时才构成酉群,当n=1时称Golstein酉群,提供了比文献3]更简便的半环证明方法。
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| 关 键 词： | 半群 酉群 生成算子 |
| 收稿时间： | 2003-04-29 |
| 修稿时间： | 2003-04-29 |
Unitary-Semigroups of 4n-2 Order Evolution Equation |
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| ZHANG Li-xun,LIU Yong-zhi,OU Zhong-hua,DAI Zhi-yong,PENG Zeng-shou.Unitary-Semigroups of 4n-2 Order Evolution Equation[J].Journal of University of Electronic Science and Technology of China,2006,35(1):130-132. |
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| Authors: | ZHANG Li-xun LIU Yong-zhi OU Zhong-hua DAI Zhi-yong PENG Zeng-shou |
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| Affiliation: | 1.School of Optic-Electronic Information,UEST of China Chengdu 610054 |
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| Abstract: | A generating operator of 4n-2 order evolution equation is obtained and this operator generates a semigroup when 4n-2 order evolution equation is changed into one order evolution equation set. The unitary semigroups which are generated by generating operator of 4n-2 order evolution equation is discussed. The unitary semigroups (n>1) are proven true when they append an equal yoke operator norm. In particular, the semigroup (n=1) is called Golstein's unitary and a more simply probative method to Ref.3] by semiring is offered. |
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| Keywords: | semigroup unitary group generating operator |
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