Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

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

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
14.09.2016
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Language: 
Russian
Heading: 
Mathematics
UDC: 
517.51
DOI: 
10.18500/1816-9791-2016-16-3-256-262
EDN: 
WMIIFJ

Orthogonal Shift Systems in the Field of p-adic Numbers

Autors: 
Vodolasov Alexander Mikhailovich, Saratov State University
Lukomskii Sergei Feodorovich, Saratov State University
Abstract: 

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.

Key words: 
orthogonal shift systems
field of p-adic numbers
p-adic MRA
References: 
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Received: 
10.04.2016
Accepted: 
26.08.2016
Published: 
30.09.2016
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