We present a full characterisation of interpolatory mask symbols where the dilation matrix is
. The characterization involves the analysis of polyno- mial identities in two variables by means of the Bezout theorem and the Euclidean algorithm. The convergence of the associated interpolatory subdivision scheme is closely related to the existence of a corresponding interpolatory refinable function. As a special case of our theory, we present the mask symbol corresponding to the Butterfly subdivision scheme.
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