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- W1575601502 abstract "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." @default.
- W1575601502 created "2016-06-24" @default.
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- W1575601502 date "2012-11-12" @default.
- W1575601502 modified "2023-09-27" @default.
- W1575601502 title "Step refinable functions and orthogonal MRA on $p$-adic Vilenkin groups" @default.
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