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Absolute Riesz summability of Fourier series. I


Authors: G. D. Dikshit and C. S. Rees
Journal: Proc. Amer. Math. Soc. 82 (1981), 231-238
MSC: Primary 42A28; Secondary 40F05
DOI: https://doi.org/10.1090/S0002-9939-1981-0609657-1
MathSciNet review: 609657
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Abstract: In this paper we prove some theorems on the absolute summability of Fourier series which connect diverse $ \left\vert {C,\gamma } \right\vert$ results such as Bosanquet's classical theorem (1936), Mohanty (1952), and Ray (1970) and the recent $ \left\vert {R,\;\exp ({{(\log \omega )}^{\beta + 1}}),\gamma } \right\vert$ result of Nayak (1971).

It is also shown that in some sense some of the conclusions of the paper are the best possible.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0609657-1
Keywords: Fourier series, absolute Riesz summability, absolute Cesàro summability, absolute convergence, function of bounded variation, totally regular methods
Article copyright: © Copyright 1981 American Mathematical Society

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