Sets of absolute convergence of double trigonometric series

  • R. A. Avetisyan
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Abstract

We obtain a sufficient condition for a set of plane measure zero to be a set of absolute convergence (an A.C.-set) for a double trigonometric series. Specifically, let y=f(x) (0 ≤x≤2π) be a smooth curve and let\(\mathop V\limits_0^{2\pi }\) inif ′(x) t <∞. Then, any set of positive linear measure lying on this curve is an A.C.-set.

Keywords

Smooth Curve Measure Zero Linear Measure Plane Measure Trigonometric Series 
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Literature cited

  1. 1.
    N. K. Bari, Trigonometric Series, Macmillan, New York (1964).Google Scholar
  2. 2.
    I. P. Natanson, Theory of Functions of a Real Variable, Ungar, New York (1955, 1960).Google Scholar

Copyright information

© Consultants Bureau 1972

Authors and Affiliations

  • R. A. Avetisyan
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityUSSR

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