Pointwise convergence of a class of non-orthogonal wavelet expansions
Abbreviated Journal Title
Proc. Amer. Math. Soc.
non-orthogonal wavelets; Shannon's wavelet; wavelet expansions; pointwise convergence; Mathematics, Applied; Mathematics
Non-orthogonal wavelet expansions associated with a class of mother wavelets is considered. This class of wavelets comprises mother wavelets that are not necessarily integrable over the whole real line, such as Shannon's wavelet. The pointwise convergence of these wavelet expansions is investigated. It is shown that, unlike other wavelet expansions, the ones under consideration do not necessarily converge pointwise to the functions at points of continuity, unless a more stringent condition, such as bounded variation, is imposed.
Proceedings of the American Mathematical Society
"Pointwise convergence of a class of non-orthogonal wavelet expansions" (2000). Faculty Bibliography 2000s. 2876.