Fourier analysis of 2-point Hermite interpolatory subdivision schemes

Dubuc, Serge; Lemire, Daniel et Merrien, Jean-Louis (2001). « Fourier analysis of 2-point Hermite interpolatory subdivision schemes ». Journal of Fourier Analysis and Applications, 7(5), pp. 532-552.

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Résumé

Two subdivision schemes with Hermite data on Z are studied. These schemes use 2 or 7 parameters respectively depending on whether Hermite data involve only first derivatives or include second derivatives. For a large region in the parameters space, the schemes are C1 or C2 convergent or at least are convergent on the space of Schwartz distributions. The Fourier transform of any interpolating function can be computed through products of matrices of order 2 or 3. The Fourier transform is related to a specific system of functional equations whose analytic solution is unique except for a multiplicative constant. The main arguments for these results come from Paley-Wiener-Schwartz theorem on the characterization of the Fourier transforms of distributions with compact support and a theorem of Artzrouni about convergent products of matrices.

Type:	Article de revue scientifique
Mots-clés ou Sujets:	Subdivion Schemes, Fourier Transform, Distributions
Unité d'appartenance:	Télé-université > UER Science et Technologie
Déposé par:	Daniel Lemire
Date de dépôt:	08 août 2007
Dernière modification:	01 nov. 2014 02:03
Adresse URL :	http://archipel.uqam.ca/id/eprint/357