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Zeitschrift für Analysis und ihre Anwendungen

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Volume 17, Issue 4, 1998, pp. 813–830
DOI: 10.4171/ZAA/852

Published online: 1998-12-31

Asymptotic Behavior of $M$-Band Scaling Functions of Daubechies Type

N. Bi[1], L. Debnath[2] and Qiyu Sun[3]

(1) Hangzhou Normal College, Zhejiang, China
(2) University of Central Florida, Orlando, USA
(3) Zhejiang University, China

This paper deals with the asymptotic behavior of $M$-band scaling functions $^M_N\phi$ and $M$-band symbols $^M_NH$ as $M \to \infty$ for $N ≥ 2$. This is followed by pointwise convergence, and $L^p$-convergence $(1 ≤ p ≤ \infty)$ of $^M_N\phi$, and the limit function $g$ of $^M_N\phi$ as $M \to \infty$.

Keywords: Wavelets, scaling functions, refinable functions

Bi N., Debnath L., Sun Qiyu: Asymptotic Behavior of $M$-Band Scaling Functions of Daubechies Type. Z. Anal. Anwend. 17 (1998), 813-830. doi: 10.4171/ZAA/852