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A lower bound for the L 1 norm of exponential sums
Author(s) -
Pichorides S. K.
Publication year - 1974
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300008536
Subject(s) - mathematics , exponent , combinatorics , exponential function , upper and lower bounds , trigonometric polynomial , norm (philosophy) , zero (linguistics) , trigonometry , polynomial , discrete mathematics , mathematical analysis , political science , law , philosophy , linguistics
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 L 1 norm of f exceeds a fixed positive multiple of (log N /log log N ) ½ . This result improves a previous one due to H. Davenport and P. J. Cohen (the same bound with exponent ¼).