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Sbornik: Mathematics, 2016, Volume 207, Issue 9, Pages 1287–1318
DOI: https://doi.org/10.1070/SM8221 (Mi sm8221) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Affine Riesz bases and the dual function

P. A. Terekhin

Saratov State University named after N. G. Chernyshevsky
English version PDF (585 kB) Citations (5)
References:
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DOI: https://doi.org/10.1070/SM8221
Abstract: This paper is concerned with systems of functions on the unit interval which are generated by dyadic dilations and integer translations of a given function. Similar systems have a wide range of applications in the theory of wavelets, in nonlinear, and in particular, in greedy approximations, in the representation of functions by series, in problems in numerical analysis, and so on. Conditions, and in some particular cases, criteria for the generating function are given for the system to be Besselian, to form a Riesz basis or to be an orthonormal system, and separately, to be complete. For this purpose, the concept of the dual function of the generating function of a system is introduced and studied. Some of the conditions given below are easy to verify in practice, as is demonstrated by examples.
Bibliography: 25 titles.
Keywords: Riesz basis, Haar system, affine system of functions, system of dilations and translations.
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 research was carried out in the framework of the governmental target programme of the Ministry of Education and Science of the Russian Federation (project no 1.1520.2014/K) and with the financial support of the Russian Foundation for Basic Research (grant no. 16-01-00152-a).
Received: 07.02.2013 and 08.04.2016
Russian version:
Matematicheskii Sbornik, 2016, Volume 207, Number 9, Pages 111–143
DOI: https://doi.org/10.4213/sm8221
Bibliographic databases:
Document Type: Article
UDC: 517.518
MSC: Primary 42C40, 46B15; Secondary 42C10, 42C15
Language: English
Original paper language: Russian
Citation: P. A. Terekhin, “Affine Riesz bases and the dual function”, Mat. Sb., 207:9 (2016), 111–143; Sb. Math., 207:9 (2016), 1287–1318
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:578
    Russian version PDF:115
    English version PDF:8
    References:55
    First page:49
     
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