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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 1, Pages 153–184 (Mi izv8181)  

This article is cited in 5 scientific papers (total in 5 papers)

Riesz multiresolution analysis on zero-dimensional groups

S. F. Lukomskii

Saratov State University named after N. G. Chernyshevsky

Abstract: On zero-dimensional groups wavelet Riesz bases with noncompact support are constructed. For Vilenkin groups a simple algorithm for constructing the scaling function in terms of the trees is obtained.

Keywords: multiresolution analysis, wavelet bases, zero-dimensional groups, Vilenkin groups.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.1520.2014/K
This paper was written within the framework of a governmental order of the Ministry of Science and Education of Russia (project no. 1.1520.2014/K).


DOI: https://doi.org/10.4213/im8181

Full text: PDF file (677 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2015, 79:1, 145–176

Bibliographic databases:

UDC: 517.518+519.688
MSC: 42C40, 43A70, 11R56
Received: 24.10.2013

Citation: S. F. Lukomskii, “Riesz multiresolution analysis on zero-dimensional groups”, Izv. RAN. Ser. Mat., 79:1 (2015), 153–184; Izv. Math., 79:1 (2015), 145–176

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/izv/v79/i1/p153

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. F. Lukomskii, G. S. Berdnikov, “$N$-valid trees in wavelet theory on Vilenkin groups”, Int. J. Wavelets Multiresolut. Inf. Process., 13:5 (2015), 1550037, 23 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    2. G. S. Berdnikov, “Grafy s konturami v kratnomasshtabnom analize na gruppakh Vilenkina”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 16:4 (2016), 377–388  mathnet  crossref  mathscinet  elib
    3. N. Kholshchevnikova, V. Skvortsov, “On $U$- and $M$-sets for series with respect to characters of compact zero-dimensional groups”, J. Math. Anal. Appl., 446:1 (2017), 383–394  crossref  mathscinet  zmath  isi  elib  scopus
    4. G. S. Berdnikov, “Necessary and sufficient condition for an orthogonal scaling function on Vilenkin groups”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 19:1 (2019), 24–33  mathnet  crossref  elib
    5. G. S. Berdnikov, S. F. Lukomskii, “Discrete orthogonal and Riesz refinable functions on local fields of positive characteristic”, Eur. J. Math., 6:4 (2020), 1505–1522  crossref  mathscinet  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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