## Taiwanese Journal of Mathematics

### ZEROS OF FINITE WAVELET SUMS

Noli N. Reyes

#### Abstract

For certain analytic functions $\psi$, a lower Riesz bound for a finite wavelet system generated by $\psi$, yields an upper bound for the number of zeros on a bounded interval of the corresponding wavelet sums. In particular, we show that if the Fourier transform of $\psi$ is compactly supported, say on $[-\Omega,\Omega]$, and if $B \gt 2e \Omega$, then any finite sum $\sum_{|k| \leq \alpha/2} a_{k} \psi(x-k)$ cannot have more than $B \alpha$ zeros in $[-\alpha,\alpha]$ for $\alpha \gt 0$ sufficiently large.

#### Article information

Source
Taiwanese J. Math., Volume 9, Number 1 (2005), 67-72.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500407745

Digital Object Identifier
doi:10.11650/twjm/1500407745

Mathematical Reviews number (MathSciNet)
MR2122903

Zentralblatt MATH identifier
1077.42031

Subjects
Primary: 41A 42A

#### Citation

Reyes, Noli N. ZEROS OF FINITE WAVELET SUMS. Taiwanese J. Math. 9 (2005), no. 1, 67--72. doi:10.11650/twjm/1500407745. https://projecteuclid.org/euclid.twjm/1500407745

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