We consider a class of (N, M )-elementary step functions on the p-adic Vilenkin group. We prove that (N, M )-elementary step function generates a MRA on p-adic Vilenkin group if and only if it is generated by a special N -valid rooted tree on the set of vertices {0, 1, . . . p − 1} with the vector (0, . . . , 0) ∈ Z N as a root.
We present a new method for constructing an orthogonal step scaling function on local fields of positive characteristic, which generates multiresolution analysis.
We propose a method to construct Riesz MRA on local fields of positive characteristic and corresponding scaling step functions that generate it Bibliography: 20 titles.
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