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Fourier analysis of 2-point Hermite interpolatory subdivision schemes [r-libre/217]

Dubuc, Serge; Lemire, Daniel, & Merrien, Jean-Louis (2001). Fourier analysis of 2-point Hermite interpolatory subdivision schemes. Journal of Fourier Analysis and Applications, 7 (5), 532-552. https://doi.org/10.1007/BF02511225

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Item Type: Journal Articles
Refereed: Yes
Status: Published
Abstract: 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.
Official URL: http://www.springerlink.com/content/g17n614wl6j37m...
Depositor: Lemire, Daniel
Owner / Manager: Daniel Lemire
Deposited: 08 Aug 2007
Last Modified: 16 Jul 2015 00:47

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