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On a theorem of Ingham on nonharmonic Fourier series


Author: Robert M. Young
Journal: Proc. Amer. Math. Soc. 92 (1984), 549-553
MSC: Primary 42C15
DOI: https://doi.org/10.1090/S0002-9939-1984-0760944-9
MathSciNet review: 760944
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Abstract: A well-known result due to Ingham [3] shows that the system of complex exponentials $ \{ {e^{i\lambda _{n}t}}\} $ is a basic sequence in $ {L^2}( - \pi ,\pi )$ whenever $ {\lambda _{n + 1}} - {\lambda _n} \geqslant \gamma > 1$. In this note, we show that the system need not be basic if $ {\lambda _{n + 1}} - {\lambda _n} > 1$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0760944-9
Keywords: Nonharmonic Fourier series, basic sequence, biorthogonal system
Article copyright: © Copyright 1984 American Mathematical Society

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