Abstract: 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 Φ 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.

Key words: poly-scale function, dilation factor, poly-scale functional equation