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Trigonometric wavelets for Hermite interpolation


Author: Ewald Quak
Journal: Math. Comp. 65 (1996), 683-722
MSC (1991): Primary 42A15, 41A05, 65D05
DOI: https://doi.org/10.1090/S0025-5718-96-00719-3
MathSciNet review: 1333324
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Abstract: The aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials. The pair of scaling functions which span the sample spaces are fundamental functions for Hermite interpolation on a dyadic partition of nodes on the interval $[0,2\pi )$. Two wavelet functions that generate the corresponding orthogonal complementary subspaces are constructed so as to possess the same fundamental interpolatory properties as the scaling functions. Together with the corresponding dual functions, these interpolatory properties of the scaling functions and wavelets are used to formulate the specific decomposition and reconstruction sequences. Consequently, this trigonometric multiresolution analysis allows a completely explicit algorithmic treatment.


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Additional Information

Ewald Quak
Affiliation: Center for Approximation Theory, Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Email: quak@math.tamu.edu

DOI: https://doi.org/10.1090/S0025-5718-96-00719-3
Keywords: Trigonometric wavelets, Hermite interpolation, decomposition and reconstruction sequences and algorithms
Received by editor(s): May 4, 1994
Received by editor(s) in revised form: October 23, 1994
Article copyright: © Copyright 1996 American Mathematical Society

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