Abstract
We prove several results that characterize the rate at which wavelet and multiresolution expansions converge to functions in a given Sobolev space in the supremum error norm. Some of the results are proved without assuming the existence of a scaling function in the multiresolution analysis. Necessary and sufficient conditions are given for convergence at given rates in terms of behavior of Fourier transforms of the wavelet or scaling function near the origin. Such conditions turn out in special cases to be equivalent to moment and other known determining convergence rates.
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Kon, M.A., Raphael, L.A. (2001). Convergence Rates of Multiscale and Wavelet Expansions. In: Debnath, L. (eds) Wavelet Transforms and Time-Frequency Signal Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0137-3_2
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DOI: https://doi.org/10.1007/978-1-4612-0137-3_2
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