| 多-尺度加细函数及其性质的研究 |
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| 引用本文： | 杨守志. 多-尺度加细函数及其性质的研究[J]. 应用数学和力学, 2006, 27(12): 1477-1485 |
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| 作者姓名： | 杨守志 |
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| 作者单位： | 汕头大学 数学系,广东 汕头 515063 |
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| 基金项目： | 广东省自然科学基金;广东省自然科学基金 |
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| 摘 要： | 引入伸缩因子为a的多-尺度加细函数和平移不变子空间的概念．研究了多-尺度加细方程解存在的条件．特别地,给出这种方程的解是正交的充分必要条件．建立了多-尺度加细函数与两尺度加细函数之间的关系．并讨论了它们的一些性质．最后给出相应的构造算例．
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| 关 键 词： | 多-尺度加细函数 伸缩因子 多-尺度加细方程 |
| 文章编号： | 1000-0887（2006）12-1477-09 |
| 收稿时间： | 2004-11-16 |
| 修稿时间： | 2006-08-18 |
Poly-Scale Refinable Function and Their Properties |
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| YANG Shou-zhi. Poly-Scale Refinable Function and Their Properties[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1477-1485 |
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| Authors: | YANG Shou-zhi |
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| Affiliation: | Department of Mathematics, Shantou University, Shantou, Guangdong 515063, P. R. China |
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| Abstract: | Poly-scale refinable function with dilation factor a was introduced. The existence of solutions of poly-scale refmable equation was investigated. Specially, necessary and sufficient conditions for the orthonommlity of solution function phi of a poly-scale refinable equation with integer dilation factor a were established. Some properties of poly-scale refinable function were discussed. Several examples illustrating how to use the method to construct poly-scale refinable function were given. |
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| Keywords: | poly-scale function dilation factor poly-scale refinable equation |
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