2012/11/12 by С. Ф. Лукомский, S. F. Lukomskii, Lukomskii, S. F. · 2 citations
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #advanced mathematical theories #math.FA
paper · pdf · doi:10.48550/arxiv.1211.2633
24 page
arxiv created 2012/11/12 · openalex publication_date 2012/11/12 · arxiv updated 2012/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We find the necessary and sufficient conditions for refinable step function under which this function generates an orthogonal MRA in the L2(\mathfrak G) -spaces on Vilenkin groups \mathfrak G. We consider a class of refinable step functions for which the mask m0(χ) is constant on cosets \mathfrak G-1^\bot and its modulus |m0(χ)| takes two values only: 0 and 1. We will prove that any refinable step function φ from this class that generates an orthogonal MRA on p-adic Vilenkin group \mathfrak G has Fourier transform with condition \rm supp φ(χ)⊂ \mathfrak Gp-2^\bot. We show the sharpness of this result too.