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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Uniqueness of Haar series which are $ (C,\,1)$ summable to Denjoy integrable functions


Author: William R. Wade
Journal: Trans. Amer. Math. Soc. 176 (1973), 489-498
MSC: Primary 42A62
MathSciNet review: 0312142
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Abstract: A Haar series $ \Sigma \;{a_k}{\chi _k}$ satisfies Condition H if $ {a_k}{\chi _k}/k \to 0$ uniformly as $ k \to \infty $. We show that if such a series is (C, 1) summable to a Denjoy integrable function f, except perhaps on a countable subset of [0, l], then that series must be the Denjoy-Haar Fourier series of f.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0312142-8
Keywords: Harr functions, Denjoy integral, (C, 1) summable
Article copyright: © Copyright 1973 American Mathematical Society