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Trigonometric Wavelets for Hermite Interpolation

Ewald Quak
Mathematics of Computation
Vol. 65, No. 214 (Apr., 1996), pp. 683-722
Stable URL: http://www.jstor.org/stable/2153608
Page Count: 40
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Trigonometric Wavelets for Hermite Interpolation
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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, 2π). 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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