Abstract
Gibbs' phenomenon occurs for most orthogonal wavelet expansions. It is also shown to occur with many wavelet interpolating series, and a characterization is given. By introducing modifications in such a series, it can be avoided. However, some series that exhibit Gibbs' phenomenon for orthogonal series do not for the associated sampling series.
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Communicated by John J. Benedetto
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Walter, G.G., Shim, HT. Gibbs' phenomenon for sampling series and what to do about it. The Journal of Fourier Analysis and Applications 4, 357–375 (1998). https://doi.org/10.1007/BF02476033
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DOI: https://doi.org/10.1007/BF02476033