Abstract
When a sampling theorem holds in wavelet subspaces, sampling expansions can be a good approximation to projection expansions. Even when the sampling theorem does not hold, the scaling function series with the usual coefficients replaced by sampled function values may also be a good approximation to the projection. We refer to such series as hybrid sampling series. For this series, we shall investigate the local convergence and analyze Gibbs phenomenon.
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This work was supported by Korea Research Foundation Grant (KRF-99-003-D00014)
HongTae Shim received BS from DanKook University and both MS and Ph. D from the University of Wisconsin-Milwaukee under the supervision of Professor Gilbert G. Walter. His research interests center on wavelet theories, Sampling theories and Gibbs' phenomenon for series of special functions.
Gilbert G. Walter received MS and Ph. D from the University of Wisconsin-Madison under the supervision of Professor Jacob Korevaar. His research area covers various parts of pure and applied mathematics such as distribution theory, statistics, wavelet theory, sampling theory, etc., He has published more than 100 papers and written three books. Now he is retired but still enjoying his research and taking mathematical travels.
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Shim, HT., Walter, G.G. Hybrid sampling series associated with orthogonal wavelets and Gibbs phenomenon. JAMC 12, 199–209 (2003). https://doi.org/10.1007/BF02936192
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DOI: https://doi.org/10.1007/BF02936192