Two-direction poly-scale refinability

Authors:
Shouzhi Yang;Yanmei Xue
Affiliations:
Department of Mathematics, Shantou University, Shantou 515063, PR China;Department of Mathematics, Shantou University, Shantou 515063, PR China
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

The concept of two-direction poly-scale refinable functions with dilation factor a and shift invariant spaces is introduced. The existence of solutions of two-direction poly-scale refinable equations is investigated. In particular, a necessary and sufficient condition for the orthonormality of the solutions is established. Some properties of two-direction poly-scale refinable functions are discussed. Finally, two examples of two-direction poly-scale refinable functions are given.