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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the integrability of complex trigonometric series

Authors: William O. Bray and Vera B. Stanojevic
Journal: Proc. Amer. Math. Soc. 93 (1985), 51-58
MSC: Primary 42A20; Secondary 42A32
MathSciNet review: 766526
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Abstract: The classical criterion for the Fourier character of cosine series and sine series is generalized to complex trigonometric series. Our treatment unifies the ideas applied to cosine and sine series. A notion of complex convex sequences is developed generalizing a result of Young [1] concerning the integrability of cosine series.

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Keywords: Integrability of trigonometric series, $ {L^1}$-convergence of Fourier series, complex monotone sequences, complex convex sequences
Article copyright: © Copyright 1985 American Mathematical Society