RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 1976, Volume 19, Issue 2, Pages 179–186 (Mi mz7737)  

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

An example of a zero series expansion in the Walsh system

V. A. Skvortsov

M. V. Lomonosov Moscow State University

Abstract: We construct an example of a zero series expansion in the Walsh system which converges to zero outside some closed $M$ set of zero measure and converges to $+\infty$ at each point of this set. This shows, in particular, that in the theorem which says that a Walsh series which converges everywhere to a finite symmetric function is a Fourier series it is impossible to omit the requirement of finiteness and allow convergence of the series on a set of zero measure to an infinity of specified sign.

Full text: PDF file (511 kB)

English version:
Mathematical Notes, 1976, 19:2, 108–112

Bibliographic databases:

UDC: 517
Received: 05.02.1975

Citation: V. A. Skvortsov, “An example of a zero series expansion in the Walsh system”, Mat. Zametki, 19:2 (1976), 179–186; Math. Notes, 19:2 (1976), 108–112

Citation in format AMSBIB
\Bibitem{Skv76}
\by V.~A.~Skvortsov
\paper An example of a~zero series expansion in the Walsh system
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 2
\pages 179--186
\mathnet{http://mi.mathnet.ru/mz7737}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=410246}
\zmath{https://zbmath.org/?q=an:0334.42019|0329.42011}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 2
\pages 108--112
\crossref{https://doi.org/10.1007/BF01098741}


Linking options:
  • http://mi.mathnet.ru/eng/mz7737
  • http://mi.mathnet.ru/eng/mz/v19/i2/p179

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. A. A. Talalyan, R. I. Ovsepian, “The representation theorems of D. E. Men'shov and their impact on the development of the metric theory of functions”, Russian Math. Surveys, 47:5 (1992), 13–47  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. N. N. Kholshchevnikova, “On the category of $\mathcal U$-sets for series in the Walsh system”, Math. Notes, 53:5 (1993), 539–554  mathnet  crossref  mathscinet  zmath  isi  elib
    3. M. G. Grigoryan, “On an orthonormal system”, Russian Math. (Iz. VUZ), 46:4 (2002), 22–26  mathnet  mathscinet  zmath  elib
  • Математические заметки Mathematical Notes
    Number of views:
    This page:146
    Full text:65
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020