Linear transforms supporting circular convolution over a commutative ring with identity

Nessibi, Mohamed Mounir. "Linear transforms supporting circular convolution over a commutative ring with identity." Commentationes Mathematicae Universitatis Carolinae 36.2 (1995): 395-400. <http://eudml.org/doc/247711>.

@article{Nessibi1995,
abstract = {We consider a commutative ring $\operatorname\{R\}$ with identity and a positive integer $\operatorname\{N\}$. We characterize all the 3-tuples $(\operatorname\{L\}_1,\operatorname\{L\}_2,\operatorname\{L\}_3)$ of linear transforms over $\operatorname\{R\}^\{\operatorname\{N\}\}$, having the “circular convolution” property, i.eṡuch that $x\ast y=\operatorname\{L\}_3(\operatorname\{L\}_1 (x)\otimes \operatorname\{L\}_2 (y))$ for all $x,y \in \operatorname\{R\}^\{\operatorname\{N\}\}$.},
author = {Nessibi, Mohamed Mounir},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {circular convolution property; Fourier transformation; circular convolution; commutative ring; linear transformations},
language = {eng},
number = {2},
pages = {395-400},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Linear transforms supporting circular convolution over a commutative ring with identity},
url = {http://eudml.org/doc/247711},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Nessibi, Mohamed Mounir
TI - Linear transforms supporting circular convolution over a commutative ring with identity
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 2
SP - 395
EP - 400
AB - We consider a commutative ring $\operatorname{R}$ with identity and a positive integer $\operatorname{N}$. We characterize all the 3-tuples $(\operatorname{L}_1,\operatorname{L}_2,\operatorname{L}_3)$ of linear transforms over $\operatorname{R}^{\operatorname{N}}$, having the “circular convolution” property, i.eṡuch that $x\ast y=\operatorname{L}_3(\operatorname{L}_1 (x)\otimes \operatorname{L}_2 (y))$ for all $x,y \in \operatorname{R}^{\operatorname{N}}$.
LA - eng
KW - circular convolution property; Fourier transformation; circular convolution; commutative ring; linear transformations
UR - http://eudml.org/doc/247711
ER -