Abstract
an orthogonal MRA for which the support of the Fou� rier transform of the scaling function is contained inside a ball of radius p N . In [13], conditions on scaling functions under which these functions generate bior� thogonal wavelets were obtained, but particular algo� rithms for constructing them were not specified. This paper considers construction of wavelet Riesz bases on Vilenkin groups for which the support of the Fourier transform of the scaling function is obtained by “spreading” the unit ball with preserving it mea� sure. We describe a simple construction of such sup� ports and the corresponding scaling functions in terms of trees. Moreover, we show that each tree with root at zero generates a scaling function.
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