Poly-Scale Refinable Function and Their Properties
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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.Abstract: Poly-scale refinable function with dilation factor a was introduced. The existence of solutions of poly-scale refinable equation was investigated. Specially, necessary and sufficient conditions for the orthonormality 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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Key words:
- poly-scale function /
- dilation factor /
- poly-scale refinable equation
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