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Proceedings of the American Mathematical Society

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The absolute summability of Fourier series of a function of Wiener's class by Nörlund means


Authors: S. N. Lal and Siya Ram
Journal: Proc. Amer. Math. Soc. 67 (1977), 87-94
MSC: Primary 42A24
DOI: https://doi.org/10.1090/S0002-9939-1977-0454502-X
MathSciNet review: 0454502
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Abstract: In this paper we prove that under suitable restrictions on $ \{ {p_n}\} $ and the integral modulus of continuity of a function f of Wiener's class the Fourier series of f is summable $ \vert N,{p_n}\vert$.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0454502-X
Keywords: Wiener's class $ {V_r}$, summable $ \vert N,{p_n}\vert$, Parseval's relation, modulus of continuity, integral modulus of continuity
Article copyright: © Copyright 1977 American Mathematical Society