Cite this article as:
Vodolasov A. M., Lukomskii S. F. Orthogonal Shift Systems in the Field of p-adic Numbers. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2016, vol. 16, iss. 3, pp. 256-262. DOI: https://doi.org/10.18500/1816-9791-2016-16-3-256-262
Orthogonal Shift Systems in the Field of p-adic Numbers
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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