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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 2, Pages 187–200 (Mi izv331)  

This article is cited in 3 scientific papers (total in 3 papers)

Function systems obtained using translates and dilates of a single function in the paces $E_\varphi$ with $\lim_{t\to\infty}\frac{\varphi(t)}t=0$

V. I. Filippov

Saratov State University named after N. G. Chernyshevsky

Abstract: We solve Ul'yanov's problem [1] of representing elements of class $\varphi(L)$ as series with respect to arbitrary function systems.

DOI: https://doi.org/10.4213/im331

Full text: PDF file (740 kB)
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English version:
Izvestiya: Mathematics, 2001, 65:2, 389–402

Bibliographic databases:

MSC: 41A30, 41A65, 42C10, 42C15, 46B15, 46T30
Received: 13.05.1999

Citation: V. I. Filippov, “Function systems obtained using translates and dilates of a single function in the paces $E_\varphi$ with $\lim_{t\to\infty}\frac{\varphi(t)}t=0$”, Izv. RAN. Ser. Mat., 65:2 (2001), 187–200; Izv. Math., 65:2 (2001), 389–402

Citation in format AMSBIB
\Bibitem{Fil01}
\by V.~I.~Filippov
\paper Function systems obtained using translates and dilates of a~single function in the paces~$E_\varphi$ with $\lim_{t\to\infty}\frac{\varphi(t)}t=0$
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 2
\pages 187--200
\mathnet{http://mi.mathnet.ru/izv331}
\crossref{https://doi.org/10.4213/im331}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1842844}
\zmath{https://zbmath.org/?q=an:1032.42034}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 2
\pages 389--402
\crossref{https://doi.org/10.1070/im2001v065n02ABEH000331}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33645957033}


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  • https://doi.org/10.4213/im331
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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. Bruna J., “On translation and affine systems spanning $L^1(\mathbb R)$”, J. Fourier Anal. Appl., 12:1 (2006), 71–82  crossref  mathscinet  zmath  isi  elib  scopus
    2. Filippov V.I., “Skhodimost ryadov fure v klassakh neintegriruemykh funktsii”, Nauka i obschestvo, 2011, no. 1, 39–42  elib
    3. V. I. Filippov, “Representation systems obtained using translates and dilates of a single function in multidimensional spaces $E_{\varphi}$”, Izv. Math., 76:6 (2012), 1257–1270  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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