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A lower bound for the L1 norm of exponential sums

Published online by Cambridge University Press:  26 February 2010

S. K. Pichorides
S. K. Pichorides
Affiliation:
N.R.C. DEMOCRITOS, Agia Paraskevi Attikis, Athens, Greece.
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Abstract

Let f(x) be a trigonometric polynomial with N (≥2) non-zero coefficients of absolute value not less than 1. In this paper it is proved that the L1 norm of f exceeds a fixed positive multiple of (logN/log log N)½. This result improves a previous one due to H. Davenport and P. J. Cohen (the same bound with exponent ¼).

Type
Research Article
Information
Mathematika , Volume 21 , Issue 2 , December 1974 , pp. 155 - 159
Copyright
Copyright © University College London 1974

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References

1.Davenport, H.. “On a theorem of P. J. Cohen”, Mathematika, 7 (1960), 93–97.CrossRefGoogle Scholar
2.Roth, K. F.. “On cosine polynomials corresponding to sets of integers”, Acta Arithmetica, 24 (1973), 87–98.CrossRefGoogle Scholar