In signal and image processing as well as in numerical solution of differential equations, wavelets with short support and with vanishing moments are important because they have good approximation properties and enable fast algorithms. A B-spline of order $m$ is a spline function that has minimal support among all compactly supported refinable functions with respect to a given smoothness. And recently, B. Han and Z. Shen constructed Riesz wavelet bases of $L_2\left(ℝ\right)$ with $m$ vanishing moments based on B-spline of order $m$. In our contribution, we present an adaptation of their quadratic spline-wavelets to the interval $[0,1]$ which preserves vanishing moments.

EUDML-ID : urn:eudml:doc:271295
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@article{702703,
     title = {A quadratic spline-wavelet basis on the interval},
     booktitle = {Programs and Algorithms of Numerical Mathematics},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics AS CR},
     address = {Prague},
     year = {2013},
     pages = {29-34},
     url = {http://dml.mathdoc.fr/item/702703}
}

Černá, Dana; Finěk, Václav; Šimůnková, Martina. A quadratic spline-wavelet basis on the interval, dans Programs and Algorithms of Numerical Mathematics, GDML_Books,  (2013), pp. 29-34. http://gdmltest.u-ga.fr/item/702703/