Abstract
In this paper, we introduce the concept of [Formula: see text]-dilation (dual) pseudo-splines in [Formula: see text] with dilation [Formula: see text], characterize the linear independence of the integer shifts, the subdivision schemes of polynomial reproduction and Hölder regularity for (dual) pseudo-splines with general dilation. We present a new method to determine the Hölder regularity of refinable functions with general dilation [Formula: see text]. Furthermore, we compare the regularities between pseudo-splines and dual ones.
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