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J. Korean Math. Soc. 2012; 49(2): 325-342

Printed March 1, 2012

https://doi.org/10.4134/JKMS.2012.49.2.325

Copyright © The Korean Mathematical Society.

The asymptotic behaviour of the $m$-th order cardinal $B$-spline wavelet

Ronald Kerman, Mi-Ae Kim, and Susanna Spektor

Brock University, St. Catharines, Brock University

Abstract

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It is well-known that the $m$-th order cardinal $B$-spline wavelet, $\psi_{m},$ decays exponentially. Our aim in this paper is to determine the exact rate of this decay and thereby to describe the asymptotic behaviour of $\psi_{m}$.

Keywords: cardinal $B$-spline wavelets, scaling function, exponential decay, asymptotic behaviour

MSC numbers: 41A60, 42A20, 42C40

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