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Trigonometric series with a generalized monotonicity condition |
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| Authors: | Lei Feng Vilmos Totik Song Ping Zhou |
| Institution: | 1. Institute of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310018, P. R. China 2. MTA-SZTE Analysis and Stochastics Research Group, Bolyai Institute, University of Szeged, Szeged, Hungary 3. Department of Mathematics and Statistics, University of South Florida, Florida, USA |
| 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. |
| Keywords: | Uniform convergence monotonicity mean value bounded variation decomposition |
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