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Mat. Sb., 2010, Volume 201, Number 11, Pages 3–18 (Mi msb7634)  

This article is cited in 2 scientific papers (total in 2 papers)

On the local behaviour of the multidimensional $\Lambda$-variation

A. N. Bakhvalov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Let two classes $(\Lambda^1,…,\Lambda^m)BV$ and $(M^1,…,M^m)BV$ on an interval $\Delta$ be given. In the paper, we find necessary and sufficient conditions for the $\Lambda$-variation of any function in the $M$-class, over a neighbourhood of every regular point, to tend to zero as the neighbourhood decreases.
Bibliography: 10 titles.

Keywords: generalized variation, regular point, variation over a neighbourhood.

DOI: https://doi.org/10.4213/sm7634

Full text: PDF file (526 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2010, 201:11, 1563–1578

Bibliographic databases:

Document Type: Article
UDC: 517.518.2
MSC: Primary 26B30; Secondary 26A45
Received: 25.09.2009 and 29.03.2010

Citation: A. N. Bakhvalov, “On the local behaviour of the multidimensional $\Lambda$-variation”, Mat. Sb., 201:11 (2010), 3–18; Sb. Math., 201:11 (2010), 1563–1578

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm7634
  • http://mi.mathnet.ru/eng/msb/v201/i11/p3

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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. Bakhvalov A.N., “Cesaro summation of Fourier series of functions from multidimensional Waterman classes”, Dokl. Math., 83:2 (2011), 247–249  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. Olevskyi V., Olevska Yu., “Geometric Aspects of Multiple Fourier Series Convergence on the System of Correctly Counted Sets”, Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization, eds. Mladenov I., Yoshioka A., Inst Biophysics & Biomedical Engineering Bulgarian Acad Sciences, 2018, 159–167  crossref  mathscinet  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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