Abstract
The objective of this paper is to investigate the solvability of a continuous two-scale (or refinement) equation and to characterize the solutions of the equation. In addition, the notion of continuous multiresolution analysis (or approximation), CMRA, generated by such a solution is introduced. Here, the notion of continuity follows from a standard engineering terminology, meaning that continuous-time instead of discretetime considerations are studied. This solution, also called a scalling function of the CMRA, gives rise to some dyadic wavelet, a notion introduced by Mallat and Zhong, for multilevel signal decompositions.
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