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arXiv:1303.5635 [math.FA]AbstractReferencesReviewsResources

Trees in Wavelet analysis on Vilenkin groups

S. F. Lukomskii

Published 2013-03-22Version 1

We consider a class of $(1,M)$-elementary step functions on the $p$-adic Vilenkin group. We prove that $(1,M)$-elementary step function generates a MRA on $p$-adic Vilenkin group iff it is generated by a rooted tree on the set of vertices $\{0,1,\dots p-1\}$ with 0 as a root. Bibliography: 14 titles.

Comments: arXiv admin note: substantial text overlap with arXiv:1211.2633
Categories: math.FA
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