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Title: Interpolatory periodic scaling functions and wavelets
Authors: KOK CHI WEE
Keywords: interpolatory, scaling function, wavelet, multiresolution, orthonormal basis, Riesz basis
Issue Date: 24-Dec-2004
Citation: KOK CHI WEE (2004-12-24). Interpolatory periodic scaling functions and wavelets. ScholarBank@NUS Repository.
Abstract: This thesis examines the theory of periodic multiple scaling functions and wavelets, and it subject to interpolatory conditions. There are several highlights. The first is a necessary and sufficient condition for the existence of interpolatory wavelets, coupled with a formula for such wavelets. Next is the role of interpolating heights on the existence of interpolatory wavelets forming orthonormal and Riesz bases for $L^2[0,2\pi)$. Motivated by the de la Vall??e Poussin means of the Dirichlet kernels, another highlight is a general family of multiresolutions with scaling functions having combinations of properties like interpolation and orthonormality. From this family, interpolatory orthonormal bases and interpolatory Riesz bases are constructed.
Appears in Collections:Master's Theses (Open)

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