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Regulated Functions Whose Fourier Series Converge for Every Change of Variable

✍ Scribed by Pamela B. Pierce; Daniel Waterman

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 261 KB
Volume: 214
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5627

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✦ Synopsis

For any continuous and 2-periodic function f, the GW condition is known to be necessary and sufficient for the everywhere convergence of the Fourier series of w x f(g for every homeomorphism g of y , with itself. It is shown that we may replace the continuous functions in this result by those which have right and left limits at each point.

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Rate of Convergence for the Absolutely (C, α) Summable Fourier Series of Functions of Bounded Variation

✍ Natalia Humphreys; Ranko Bojanic 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 97 KB

A theorem of Bosanquet states that the Fourier series of a 2?-periodic function of bounded variation is absolutely (C, :) summable. In this paper we give a quantitative version of Bosanquet's result.