Uniqueness of Haar series which are $(C, 1)$ summable to Denjoy integrable functions
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- by William R. Wade PDF
- Trans. Amer. Math. Soc. 176 (1973), 489-498 Request permission
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.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 176 (1973), 489-498
- MSC: Primary 42A62
- DOI: https://doi.org/10.1090/S0002-9947-1973-0312142-8
- MathSciNet review: 0312142