Classification of Refinable Splines
نویسندگان
چکیده
A refinable spline is a compactly supported refinable function that is piecewise polynomial. Refinable splines, such as the well known B-splines, play a key role in computer aided geometric designs. So far all studies on refinable splines have focused on positive integer dilations and integer translations, and under this setting a rather complete classification was obtained in [12]. However, refinable splines do not have to have integer dilations and integer translations. The classification of refinable splines with non-integer dilations and arbitrary translations are studied in this paper. We classify completely all refinable splines with integer translations with arbitrary dilations. Our study involves techniques from number theory and complex analysis.
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