Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/14389
 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. URI: http://scholarbank.nus.edu.sg/handle/10635/14389 Appears in Collections: Master's Theses (Open)

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