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Zbl 1117.65179
Cattani, C.
Connection coefficients of Shannon wavelets. (English)
[J] Math. Model. Anal. 11, No. 2, 117-132 (2006). ISSN 1392-6292; ISSN 1648-3510/e

The paper presents an explicit computation of the matrix coefficients representing differential operators of arbitrary order in a Shannon wavelet basis. Shannon wavelets for which explicit expressions are available in physical and in Fourier space form an orthogonal basis of $L^2(\Bbb R)$. They are compactly supported in Fourier space, exhibit a $1/x$ decay in physical space and they can be derived from harmonic wavelets. The entries of the stiffness matrix required e.g. for Galerkin discretizations of differential equations fulfill recursion formulas. In the present paper they are called connection coefficients, in the literature, however, this expression is used for the coefficients representing bilinear terms in a wavelet basis, i.e. the projection of the square of a wavelet onto a wavelet.
[Kai Schneider (Marseille)]

MSC 2000:: *65T60 Wavelets
65M60 Finite numerical methods (IVP of PDE)
94A11 Application of orthogonal functions in communication
42C40 Wavelets

Keywords: Shannon wavelets; Galerkin methods; differential operators

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