| 广义Sierpinski垫正交指数集的元素个数 |
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| 引用本文： | 于雪莉,袁彦波,梁菊花. 广义Sierpinski垫正交指数集的元素个数[J]. 黑龙江科技学院学报, 2009, 19(2): 140-142 |
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| 作者姓名： | 于雪莉 袁彦波 梁菊花 |
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| 作者单位： | 陕西师范大学,数学与信息科学学院,西安,710062 |
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| 基金项目： | 周口师范学院青年科研基金重点项目 |
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| 摘 要： | 针对广义Sierpinski垫正交指数函数集的元素个数问题,引入自仿测度概念,将Dutkay和Jorgensen所讨论的扩张矩阵M推广,通过分析μM,D的傅里叶变换M,D的零点集Z（M,D）的性质,证明L2（μM,D）中的任意正交指数集至多包含4个元素。这一结论改进并推广了以前的相关结果。
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| 关 键 词： | 自仿测度 迭代函数系 正交指数函数 |
Number of elements of orthogonal exponentials on generalized Sierpinski gasket |
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| YU Xueli,YUAN Yanbo,LIANG Juhua. Number of elements of orthogonal exponentials on generalized Sierpinski gasket[J]. Journal of Heilongjiang Institute of Science and Technology, 2009, 19(2): 140-142 |
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| Authors: | YU Xueli YUAN Yanbo LIANG Juhua |
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| Affiliation: | College of Mathematics and Information Science;Shanxi Normal University;Xi'an 710062;China |
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| Abstract: | In order to study the problem of the number of the orthogonal exponential functions on the generalized Sierpinski gasket, the concept of self-affine measure is introduced. By the analysis of characterization of the zero set Z（μM,D） of the Fourier transformμM,D, it is proved that there exist at most 4 mutually orthogonal exponentials in L2 （μM,D）. The previous relevant results are improved and extended. |
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| Keywords: | self-affine measure iterated function system orthogonal exponentials |
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