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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, Volume 16, Issue 3, Pages 247–256
DOI: https://doi.org/10.18500/1816-9791-2016-16-3-247-256 (Mi isu642) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Affine system of Walsh type. Completeness and minimality

Kh. H. H. Al-Jouranya, V. A. Mironovb, P. A. Terekhinb

a University of Diyala, Baquba, Diyala Province, Iraq
b Saratov State University, 83, Astrakhanskaya st., 410012, Saratov, Russia
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DOI: https://doi.org/10.18500/1816-9791-2016-16-3-247-256
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.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.1520.2014/К
Russian Foundation for Basic Research 16-01-00152_а
This work of Kh. H. H. Al-Jourany was supported by the Iraq Ministry of High Education and Scientific Research. This work of V. A. Mironov and P. A. Terekhin were supported by the Russian Ministry of Science and Education (projects no. 1.1520.2014/К). This work of P. A. Terekhin was supported by the Russian Foundation for Basic Research (projects no. 16-01-00152).
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: Kh. H. H. Al-Jourany, V. A. Mironov, P. A. Terekhin, “Affine system of Walsh type. Completeness and minimality”, Izv. Saratov Univ. Math. Mech. Inform., 16:3 (2016), 247–256
Citation in format AMSBIB
\Bibitem{Al-MirTer16}
\by Kh.~H.~H.~Al-Jourany, V.~A.~Mironov, P.~A.~Terekhin
\paper Affine system of Walsh type. Completeness and minimality
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2016
\vol 16
\issue 3
\pages 247--256
\mathnet{http://mi.mathnet.ru/isu642}
\crossref{https://doi.org/10.18500/1816-9791-2016-16-3-247-256}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3557751}
\elib{https://elibrary.ru/item.asp?id=26702013}
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    • This publication is cited in the following 1 articles:
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    		Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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