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Mat. Sb., 2010, Volume 201, Number 5, Pages 41–64 (Mi msb7580)  

This article is cited in 12 scientific papers (total in 12 papers)

Multiresolution analysis on zero-dimensional Abelian groups and wavelets bases

S. F. Lukomskii

Saratov State University named after N. G. Chernyshevsky

Abstract: For a locally compact zero-dimensional group $(G,\mathbin{\dot+})$, we build a multiresolution analysis and put forward an algorithm for constructing orthogonal wavelet bases. A special case is indicated when a wavelet basis is generated from a single function through contractions, translations and exponentiations.
Bibliography: 19 titles.

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

DOI: https://doi.org/10.4213/sm7580

Full text: PDF file (581 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2010, 201:5, 669–691

Bibliographic databases:

UDC: 517.518.34+517.518.36+517.986.62
MSC: Primary 42C40; Secondary 46B15, 42C05, 43A15
Received: 21.05.2009 and 07.07.2009

Citation: S. F. Lukomskii, “Multiresolution analysis on zero-dimensional Abelian groups and wavelets bases”, Mat. Sb., 201:5 (2010), 41–64; Sb. Math., 201:5 (2010), 669–691

Citation in format AMSBIB
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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. Lukomskii S.F., “Haar system on a product of zero-dimensional compact groups”, Cent. Eur. J. Math., 9:3 (2011), 627–639  crossref  mathscinet  zmath  isi  elib  scopus
    2. S. F. Lukomskii, “Neortogonalnyi kratnomasshtabnyi analiz na nul-mernykh lokalno kompaktnykh gruppakh”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 11:3(1) (2011), 25–32  mathnet  elib
    3. Lukomskii S.F., “Multiresolution analysis on product of zero-dimensional Abelian groups”, J. Math. Anal. Appl., 385:2 (2012), 1162–1178  crossref  mathscinet  zmath  isi  elib  scopus
    4. I. Ya. Novikov, M. A. Skopina, “Why Are Haar Bases in Various Structures the Same?”, Math. Notes, 91:6 (2012), 895–898  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. S. S. Platonov, “On spectral synthesis on zero-dimensional Abelian groups”, Sb. Math., 204:9 (2013), 1332–1346  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. S. F. Lukomskii, “ep refinable functions and orthogonal MRA on Vilenkin groups”, J. Fourier Anal. Appl., 20:1 (2014), 42–65  crossref  mathscinet  zmath  isi  elib  scopus
    7. S. F. Lukomskii, “Riesz multiresolution analysis on Vilenkin groups”, Dokl. Math., 90:1 (2014), 412–415  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    8. S. F. Lukomskii, “Riesz multiresolution analysis on zero-dimensional groups”, Izv. Math., 79:1 (2015), 145–176  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. A. Barg, M. Skriganov, “Association schemes on general measure spaces and zero-dimensional Abelian groups”, Adv. Math., 281 (2015), 142–247  crossref  mathscinet  zmath  isi  elib  scopus
    10. 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  scopus
    11. 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
    12. 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
  • Математический сборник Sbornik: Mathematics (from 1967)
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