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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. | URI: | http://scholarbank.nus.edu.sg/handle/10635/14389 |
Appears in Collections: | Master's Theses (Open) |
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