On the L 1 norm of exponential sums

S. K. Pichorides

Annales de l'institut Fourier (1980)

  • Volume: 30, Issue: 2, page 79-89
  • ISSN: 0373-0956

Abstract

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The L 1 norm of a trigonometric polynomial with N non zero coefficients of absolute value not less than 1 exceeds a fixed positive multiple of C ( log N ) / ( log log N ) 2 .

How to cite

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Pichorides, S. K.. "On the $L^1$ norm of exponential sums." Annales de l'institut Fourier 30.2 (1980): 79-89. <http://eudml.org/doc/74451>.

@article{Pichorides1980,
abstract = {The $L^1$ norm of a trigonometric polynomial with $N$ non zero coefficients of absolute value not less than 1 exceeds a fixed positive multiple of $C\,(\{\rm log\}\, N)/(\{\rm log\}\,\{\rm log\}\, N)^2.$},
author = {Pichorides, S. K.},
journal = {Annales de l'institut Fourier},
keywords = {L1 norm; exponential sums},
language = {eng},
number = {2},
pages = {79-89},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the $L^1$ norm of exponential sums},
url = {http://eudml.org/doc/74451},
volume = {30},
year = {1980},
}

TY - JOUR
AU - Pichorides, S. K.
TI - On the $L^1$ norm of exponential sums
JO - Annales de l'institut Fourier
PY - 1980
PB - Association des Annales de l'Institut Fourier
VL - 30
IS - 2
SP - 79
EP - 89
AB - The $L^1$ norm of a trigonometric polynomial with $N$ non zero coefficients of absolute value not less than 1 exceeds a fixed positive multiple of $C\,({\rm log}\, N)/({\rm log}\,{\rm log}\, N)^2.$
LA - eng
KW - L1 norm; exponential sums
UR - http://eudml.org/doc/74451
ER -

References

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  1. [1] J. F. FOURIER, On a theorem of Paley and the Littlewood conjecture, To appear in Arkiv för Matematik. 
  2. [2] S. K. PICHORIDES, On a conjecture of Littlewood concerning exponential sums (I), Bull. Greek Math. Soc., Vol. 18 (1977), 8-16. Zbl0408.10025MR80d:10057a
  3. [3] S. K. PICHORIDES, On a conjecture of Littlewood concerning exponential suns (II), Bull. Greek Math. Soc., Vol. 19 (1978), 274-277. Zbl0421.10025MR80d:10057b
  4. [4] A. ZYGMUND, Trigonometric Series. Vol. I, II. Cambridge University Press, 1968. October 1979. 

NotesEmbed ?

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