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Izv. RAN. Ser. Mat., 2006, Volume 70, Issue 4, Pages 3–20 (Mi izv592)  

This article is cited in 1 scientific paper (total in 1 paper)

On local behaviour of multi-dimensional harmonic variation

A. N. Bakhvalov

M. V. Lomonosov Moscow State University

Abstract: In this paper, we study the behaviour of harmonic variation in a neighbourhood of a regular point for functions belonging to some multi-dimensional Waterman classes. As a consequence, some new results are obtained on the convergence of multiple trigonometric Fourier series for functions in these classes.

Keywords: Local extremal problems for bounded analytic nonvanishing functions; multiple Fourier series

DOI: https://doi.org/10.4213/im592

Full text: PDF file (489 kB)
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English version:
Izvestiya: Mathematics, 2006, 70:4, 641–660

Bibliographic databases:

UDC: 517.518
MSC: 26A45, 26B30, 42A20, 42A38, 42B35, 42B10
Received: 28.09.2005

Citation: A. N. Bakhvalov, “On local behaviour of multi-dimensional harmonic variation”, Izv. RAN. Ser. Mat., 70:4 (2006), 3–20; Izv. Math., 70:4 (2006), 641–660

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. N. Bakhvalov, “On the local behaviour of the multidimensional $\Lambda$-variation”, Sb. Math., 201:11 (2010), 1563–1578  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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