Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
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Vodolasov A. M., Lukomskii S. F. Orthogonal Shift Systems in the Field of p-adic Numbers. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 3, pp. 256-262. DOI: 10.18500/1816-9791-2016-16-3-256-262, EDN: WMIIFJ

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Orthogonal Shift Systems in the Field of p-adic Numbers

Vodolasov Alexander Mikhailovich, Saratov State University
Lukomskii Sergei Feodorovich, Saratov State University

In 2010 S. Albeverio, S. Evdokimov and M. Skopina proved that if the shift system (ϕ(x−˙ h)) of a step function ϕ is orthonormal and ϕ generates p-adic MRA then its Fourier transform lies in the unit ball. We prove then in some cases the condition "ϕ 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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