A note on the convolution theorem for the Fourier transform
Czechoslovak Mathematical Journal (2011)
- Volume: 61, Issue: 1, page 199-207
- ISSN: 0011-4642
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topKahane, Charles S.. "A note on the convolution theorem for the Fourier transform." Czechoslovak Mathematical Journal 61.1 (2011): 199-207. <http://eudml.org/doc/196654>.
@article{Kahane2011,
abstract = {In this paper we characterize those bounded linear transformations $Tf$ carrying $L^\{1\}( \mathbb \{R\}^\{1\}) $ into the space of bounded continuous functions on $\mathbb \{R\}^\{1\}$, for which the convolution identity $T(f\ast g) =Tf\cdot Tg $ holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.},
author = {Kahane, Charles S.},
journal = {Czechoslovak Mathematical Journal},
keywords = {convolution; Fourier transform; convolution; Fourier transform},
language = {eng},
number = {1},
pages = {199-207},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on the convolution theorem for the Fourier transform},
url = {http://eudml.org/doc/196654},
volume = {61},
year = {2011},
}
TY - JOUR
AU - Kahane, Charles S.
TI - A note on the convolution theorem for the Fourier transform
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 1
SP - 199
EP - 207
AB - In this paper we characterize those bounded linear transformations $Tf$ carrying $L^{1}( \mathbb {R}^{1}) $ into the space of bounded continuous functions on $\mathbb {R}^{1}$, for which the convolution identity $T(f\ast g) =Tf\cdot Tg $ holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.
LA - eng
KW - convolution; Fourier transform; convolution; Fourier transform
UR - http://eudml.org/doc/196654
ER -
References
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- Krantz, S., A Panorama of Harmonic Analysis, The Carus Mathematical Monographs, Number 27, The Mathematical Association of America, Washington D.C. (1999). (1999) MR1710388
- Rudin, W., Real and Complex Analysis, McGraw-Hill, New York, 1st edition (1966). (1966) Zbl0142.01701MR0210528
- Stein, E. M., Shakarchi, R., Real Analysis, Princeton University Press, Princeton, New Jersey (2005). (2005) Zbl1081.28001MR2129625
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