Journal of Fourier Analysis and Applications

, Volume 7, Issue 5, pp 537–552

# Fourier analysis of 2-point hermite interpolatory subdivision schemes

• Serge Dubuc
• Daniel Lemire
• Jean-Louis Merrien
Article

## 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 parameter space, the schemes are convergent in 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.

## Math Subject Classifications

40A20 42A38 46F12 65D05 65D10

## Keywords and Phrases

Hermite interpolation curve fitting subdivision Fourier transform distributions convergence of infinite products products of matrices

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## Authors and Affiliations

• Serge Dubuc
• 1
• Daniel Lemire
• 2
• Jean-Louis Merrien
• 3
1. 1.Département de mathématiques et de statistiqueUniversité de MontréalMontréalCanada