A characterization of Fourier transforms
Colloquium Mathematicae (2010)
- Volume: 118, Issue: 2, page 569-580
- ISSN: 0010-1354
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topPhilippe Jaming. "A characterization of Fourier transforms." Colloquium Mathematicae 118.2 (2010): 569-580. <http://eudml.org/doc/283505>.
@article{PhilippeJaming2010,
abstract = {The aim of this paper is to show that, in various situations, the only continuous linear (or not) map that transforms a convolution product into a pointwise product is a Fourier transform. We focus on the cyclic groups ℤ/nℤ, the integers ℤ, the torus 𝕋 and the real line. We also ask a related question for the twisted convolution.},
author = {Philippe Jaming},
journal = {Colloquium Mathematicae},
keywords = {Fourier transform; convolution},
language = {eng},
number = {2},
pages = {569-580},
title = {A characterization of Fourier transforms},
url = {http://eudml.org/doc/283505},
volume = {118},
year = {2010},
}
TY - JOUR
AU - Philippe Jaming
TI - A characterization of Fourier transforms
JO - Colloquium Mathematicae
PY - 2010
VL - 118
IS - 2
SP - 569
EP - 580
AB - The aim of this paper is to show that, in various situations, the only continuous linear (or not) map that transforms a convolution product into a pointwise product is a Fourier transform. We focus on the cyclic groups ℤ/nℤ, the integers ℤ, the torus 𝕋 and the real line. We also ask a related question for the twisted convolution.
LA - eng
KW - Fourier transform; convolution
UR - http://eudml.org/doc/283505
ER -
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