A mini-gap theorem for Fourier series
Published online by Cambridge University Press: 24 October 2008
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Suppose that
belongs to L2( − π, π). If most of the coefficients vanish then f (x) cannot be too small in a certain interval without being small generally. More precisely Ingham ((2), Theorem 1) has proved the following
THEOREM A. Suppose that f (x) is given by (1·1) and that an = 0, except for a sequence n = nν, where nν+1 − nν ≥ C. Then given ∈ > 0 there exists a constant A (∈), such that we have for any real x1
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 1 , January 1968 , pp. 61 - 66
- Copyright
- Copyright © Cambridge Philosophical Society 1968
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