多-尺度加细函数及其性质的研究  

Poly-Scale Refinable Function and Their Properties

作　　者：杨守志[1] 李继彬（推荐） 

机构地区：[1]汕头大学数学系,广东汕头515063 [2]不详

出　　处：《应用数学和力学》2006年第12期1477-1485,共9页Applied Mathematics and Mechanics

基　　金：广东省自然科学基金资助项目(032038;05008289;06105648);广东省自然科学博士基金资助项目(04300917)

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·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.

关 键 词：多-尺度加细函数 伸缩因子 多-尺度加细方程 

分 类 号：O174.42[理学—数学]