On Young's criteria for the convergence of Fourier series and their conjugates
Published online by Cambridge University Press: 24 October 2008
Extract
1. Young's criterion for the convergence of a Fourier series may be stated in the following form:
The integral
tends to zero as ω → ∞ whenever
(A) ø(t) is absolutely integrable in (0, a),
(B) ø(t) → 0 in mean as t → 0,
(C) tø(t) is of bounded variation to the immediate right of t = 0 and, as t → 0,
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- Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 25 , Issue 1 , January 1929 , pp. 26 - 30
- Copyright
- Copyright © Cambridge Philosophical Society 1929
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