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Trigonometric series with a generalized monotonicity condition

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Abstract

In this paper, we consider numerical and trigonometric series with a very general monotonicity condition. First, a fundamental decomposition is established from which the sufficient parts of many classical results in Fourier analysis can be derived in this general setting. In the second part of the paper a necessary and sufficient condition for the uniform convergence of sine series is proved generalizing a classical theorem of Chaundy and Jolliffe.

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Authors and Affiliations

  1. Institute of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310018, P. R. China

    Lei Feng & Song Ping Zhou

  2. MTA-SZTE Analysis and Stochastics Research Group, Bolyai Institute, University of Szeged, Szeged, Hungary

    Vilmos Totik

  3. Department of Mathematics and Statistics, University of South Florida, Florida, USA

    Vilmos Totik

Authors
  1. Lei Feng
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  2. Vilmos Totik
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  3. Song Ping Zhou
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Corresponding author

Correspondence to Song Ping Zhou.

Additional information

Supported by the European Research Council Advanced Grant (Grant No. 267055)

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Feng, L., Totik, V. & Zhou, S.P. Trigonometric series with a generalized monotonicity condition. Acta. Math. Sin.-English Ser. 30, 1289–1296 (2014). https://doi.org/10.1007/s10114-014-3496-6

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  • DOI: https://doi.org/10.1007/s10114-014-3496-6

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