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Izv. RAN. Ser. Mat., 2007, Volume 71, Issue 1, Pages 61–78 (Mi izv739)  

This article is cited in 4 scientific papers (total in 4 papers)

On multiple Walsh series convergent over cubes

M. G. Plotnikov

M. V. Lomonosov Moscow State University

Abstract: We consider Walsh functions on the binary group $G$ and study uniqueness sets for $N$-fold multiple Walsh series under convergence over cubes (in other words, $U_{N,\mathrm{cube}}$-sets). We prove that every finite set is a $U_{N,\mathrm{cube}}$-set, construct examples of countable $U_{N,\mathrm{cube}}$-sets and non-empty perfect $U_{N,\mathrm{cube}}$-sets, and give an example of a $U_{N,\mathrm{cube}}$-set having the maximum possible Hausdorff dimension.

DOI: https://doi.org/10.4213/im739

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English version:
Izvestiya: Mathematics, 2007, 71:1, 57–73

Bibliographic databases:

UDC: 517.518.3
MSC: 41A30, 42A44, 42C10, 42C15, 42C25, 43A46
Received: 28.12.2005

Citation: M. G. Plotnikov, “On multiple Walsh series convergent over cubes”, Izv. RAN. Ser. Mat., 71:1 (2007), 61–78; Izv. Math., 71:1 (2007), 57–73

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. M. G. Plotnikov, “Quasi-measures, Hausdorff $p$-measures and Walsh and Haar series”, Izv. Math., 74:4 (2010), 819–848  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. M. G. Plotnikov, “Quasi-measures on the group $G^m$, Dirichlet sets, and uniqueness problems for multiple Walsh series”, Sb. Math., 201:12 (2010), 1837–1862  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. I. S. Yurchenko, “O mnozhestvakh edinstvennosti kratnykh ryadov po sisteme kharakterov nul-mernoi gruppy v smysle skhodimosti po kubam”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 13:2(1) (2013), 35–43  mathnet
    4. M. G. Plotnikov, “$\lambda$-Convergence of Multiple Walsh–Paley Series and Sets of Uniqueness”, Math. Notes, 102:2 (2017), 268–276  mathnet  crossref  crossref  mathscinet  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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