Poly-scale refinable function with dilation factor a is introduced. The existence of solution of poly-scale refinable equation is investigated. Specially, necessary and sufficient conditions for the orthonormality of ...Poly-scale refinable function with dilation factor a is introduced. The existence of solution of poly-scale refinable equation is investigated. Specially, necessary and sufficient conditions for the orthonormality of solution function Ф of poly-scale refinable equation with integer dilation factor a are established. Some properties of poly-scale refinable function are discussed. Several examples illustrating how to use the method to construct poly-scale refinable function are given.展开更多
基金Project supported by the Natural Science Foundation of Guangdong Province (Nos.032038, 05008289, 06105648) the Doctoral Foundation of Guangdong Province (No.04300917)
文摘Poly-scale refinable function with dilation factor a is introduced. The existence of solution of poly-scale refinable equation is investigated. Specially, necessary and sufficient conditions for the orthonormality of solution function Ф of poly-scale refinable equation with integer dilation factor a are established. Some properties of poly-scale refinable function are discussed. Several examples illustrating how to use the method to construct poly-scale refinable function are given.
