Geodesic
Orthogonal shift systems in the field of $p$-adic numbers
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 3, pp. 256-262

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In 2010 S. Albeverio, S. Evdokimov and M. Skopina proved that if the shift system $(\varphi(x\dot-h))$ of a step function $\varphi$ is orthonormal and $\varphi$ generates $p$-adic MRA then its Fourier transform lies in the unit ball. We prove then in some cases the condition "$\varphi$ generates MRA" is possible to be omitted. In general, we indicate the number of linearly independent step-functions, which shifts form an orthonormal system. 
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A. M. Vodolazov; S. F. Lukomskii. Orthogonal shift systems in the field of $p$-adic numbers. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 3, pp. 256-262. http://geodesic.mathdoc.fr/item/ISU_2016_16_3_a1/