The norm of the Fourier transform on finite abelian groups

John Gilbert[1]; Ziemowit Rzeszotnik[2]

  • [1] University of Texas Department of Mathematics Austin, TX 78712–1082 (USA)
  • [2] Wrocław University Mathematical Institute Pl. Grunwaldzki 2/4 50-384 Wrocław (Poland)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 4, page 1317-1346
  • ISSN: 0373-0956


For 1 p , q we calculate the norm of the Fourier transform from the L p space on a finite abelian group to the L q space on the dual group.

How to cite


Gilbert, John, and Rzeszotnik, Ziemowit. "The norm of the Fourier transform on finite abelian groups." Annales de l’institut Fourier 60.4 (2010): 1317-1346. <>.

abstract = {For $1\le p,q\le \infty $ we calculate the norm of the Fourier transform from the $L^p$ space on a finite abelian group to the $L^q$ space on the dual group.},
affiliation = {University of Texas Department of Mathematics Austin, TX 78712–1082 (USA); Wrocław University Mathematical Institute Pl. Grunwaldzki 2/4 50-384 Wrocław (Poland)},
author = {Gilbert, John, Rzeszotnik, Ziemowit},
journal = {Annales de l’institut Fourier},
keywords = {Fourier transform; finite abelian groups; wave packets; biunimodular functions},
language = {eng},
number = {4},
pages = {1317-1346},
publisher = {Association des Annales de l’institut Fourier},
title = {The norm of the Fourier transform on finite abelian groups},
url = {},
volume = {60},
year = {2010},

AU - Gilbert, John
AU - Rzeszotnik, Ziemowit
TI - The norm of the Fourier transform on finite abelian groups
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 4
SP - 1317
EP - 1346
AB - For $1\le p,q\le \infty $ we calculate the norm of the Fourier transform from the $L^p$ space on a finite abelian group to the $L^q$ space on the dual group.
LA - eng
KW - Fourier transform; finite abelian groups; wave packets; biunimodular functions
UR -
ER -


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