Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

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Al-Jourany K. H., Mironov V. A., Terekhin P. A. Affine System of Walsh Type. Completeness and Minimality. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 3, pp. 247-256. DOI: 10.18500/1816-9791-2016-16-3-247-256, EDN: WMIIEZ

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: 
10.18500/1816-9791-2016-16-3-247-256
EDN: 
WMIIEZ

Affine System of Walsh Type. Completeness and Minimality

Autors: 
Al-Jourany Khalid H. H., Diala University
Mironov Vyacheslav Aleksandrovich, Saratov State University
Terekhin Pavel A., Saratov State University
Abstract: 

The question on completeness and minimality of Walsh affine systems is considered. On the basis of functional-analytical structure of multishift in Hilbert space, which being the generalized analogue of the operator of simple one-side shift and closely connected with Cuntz algebra representations, we give definition of Walsh affine system. Various criteria and tests of completeness of affine systems of functions are established. A biorthogonal conjugate system is found and its completeness is proved. 

Key words: 
Walsh functions
affine system
completeness
minimality
shift operator
multishift structure
References: 
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Received: 
13.04.2016
Accepted: 
28.08.2016
Published: 
30.09.2016
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