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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the absolute convergence of lacunary Fourier series


Authors: J. R. Patadia and V. M. Shah
Journal: Proc. Amer. Math. Soc. 83 (1981), 680-682
MSC: Primary 42A38; Secondary 42A55
MathSciNet review: 630036
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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].


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0630036-5
PII: S 0002-9939(1981)0630036-5
Keywords: Lacunary Fourier series, absolute convergence, modulus of continuity, Lipschitz condition
Article copyright: © Copyright 1981 American Mathematical Society