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One of the important capabilities for a subdivision scheme is the reproducing property of circular shapes or parts of conics that are important analytical shapes in geometrical modelling. In this regards, the first goal of this study is to provide necessary and sufficient conditions for a non-stationary subdivision to have the reproducing property of… (More)

We analyze the internal structure of the multiresolution analyses of L 2 (R d) defined by the unitary extension principle (UEP) of Ron and Shen. Suppose we have a wavelet tight frame defined by the UEP. Define V 0 to be the closed linear span of the shifts of the scaling function and W 0 that of the shifts of the wavelets. Finally, define V 1 to be the… (More)

We show that the 'centered' Battle-Lemarié scaling function and wavelet of order n converge in L q (2 ≤ q ≤ ∞), uniformly in particular, to the Shannon scaling function and wavelet as n tends to the infinity.

Consider a continuous function g ∈ L 2 (R) that is supported on [−1, 1] and generates a Gabor frame with translation parameter 1 and modulation parameter 0 < b < 2N 2N +1 for some N ∈ N. Under an extra condition on the zeroset of the window g we show that there exists a continuous dual window supported on [−N, N ]. We also show that this result is optimal:… (More)