Keywords. Refinement equation, dilation equation, characteristic function.
Springer Online Journal Archives 1860-2000
Summary. There is a non-trivial integrable solution to a two scale difference equation with non-negative coefficients, if and only if the corresponding random expansion is absolutely continuous. Utilizing this characterization a simple description in terms of the coefficients is given of all refinement equations with no more than six coefficients possessing an integrable solution.
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