M. Rouff (France)
Fourier tranforms, Ckspline functions, Ck wavelets, integro-differential operators, nonentire integro-differential operators
We present in this article the principal algebraic, arithmetic and geometric properties of the Ck spline functions. Their good properties of regularity, smoothness and compactness in Fourier space, allow us to consider accurate and powerful computations involving Ck spline functions spectra in Fourier space opening the way to new algorithmics matching time and fre quencial properties of the problem. Moreover these Ck spline spectra are wavelets, with the remarkable prop erty that coefficients of their functionnal expansions are the set of the total or partial derivarives up to k of the dual functions, which for example open the way to a new easy measure of the enthropy of a signal. Appli cations to differential equations are also considered.
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