Abstract:
Approximation properties are studied for periodic Parseval wavelet frames and for corresponding families of refinable functions. Approximation properties are described in terms of the approximation orders. Necessary and sufficient conditions are given for Parseval wavelet frames and generating multiresolution analysis to provide specific approximation orders are given. Also, the relationship between the approximation orders provided by a periodic multiresolution analysis and by a wavelet frame is revealed.
Key words and phrases:Parseval wavelet frame, periodic wavelets, approximation order.
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