Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Step refinable functions and orthogonal MRA on $p$-adic Vilenkin groups   We find the necessary and sufficient conditions for refinable step function
under which this function generates an orthogonal MRA in the $L_2(\mathfrak G)$
-spaces on Vilenkin groups $\mathfrak G$. We consider a class of refinable step
functions for which the mask $m_0(\chi)$ is constant on cosets $\mathfrak
G_{-1}^\bot$ and its modulus $|m_0(\chi)|$ takes two values only: 0 and 1. We
will prove that any refinable step function $\varphi$ from this class that
generates an orthogonal MRA on $p$-adic Vilenkin group $\mathfrak G$ has
Fourier transform with condition ${\rm supp} \hat \varphi(\chi)\subset
\mathfrak G_{p-2}^\bot$. We show the sharpness of this result too.

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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con