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arXiv · 1407.4069

Non-Haar MRA on local fields of positive characteristic

Sergey Lukomskii·Alexander Vodolazov
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Abstract

We propose a simple method to construct integral periodic mask and corresponding scaling step functions that generate non-Haar orthogonal MRA on the local field $ F^{(s)}$ of positive characteristic $p$. To construct this mask we use two new ideas. First, we consider local field as vector space over the finite field $GF(p^s)$. Second, we construct scaling function by arbitrary tree that has $p^s$ vertices. By fixed prime number $p$ there exist $p^{s(p^s-2)}$ such trees.

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Sergey Lukomskii, Alexander Vodolazov. 2014-07-15. Non-Haar MRA on local fields of positive characteristic. https://arxiv.org/abs/1407.4069

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