On the absolute convergence of lacunary Fourier series
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- by J. R. Patadia and V. M. Shah PDF
- Proc. Amer. Math. Soc. 83 (1981), 680-682 Request permission
Abstract:
In 1958, P. B. Kennedy [2] proved a two-part theorem on the order of magnitude of the coefficients and the absolute convergence of lacunary Fourier series, and he conjectured that his conclusions remained valid under weaker conditions. The conjecture on the order of magnitude of the coefficients was established by M. and S. I. Izumi [1]. In this note the second half of the conjecture, concerning absolute convergence, is deduced from a recent result of Patadia [3].References
- Masako Izumi and Shin-ichi Izumi, On lacunary Fourier series, Proc. Japan Acad. 41 (1965), 648–651. MR 198099
- P. B. Kennedy, On the coefficients in certain Fourier series, J. London Math. Soc. 33 (1958), 196–207. MR 98274, DOI 10.1112/jlms/s1-33.2.196
- J. R. Patadia, On the absolute convergence of lacunary Fourier series, Proc. Amer. Math. Soc. 71 (1978), no. 1, 19–25. MR 493138, DOI 10.1090/S0002-9939-1978-0493138-2
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 680-682
- MSC: Primary 42A38; Secondary 42A55
- DOI: https://doi.org/10.1090/S0002-9939-1981-0630036-5
- MathSciNet review: 630036