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'' pro\-perty, i.e\. such that $x\ast y=\operatorname L_3(\operatorname L_1 (x)\otimes \operatorname L_2 (y))$ for all $x,y \in \operatorname R^{\operatorname N}$.
@article{118765,
author = {Mohamed Mounir Nessibi},
title = {Linear transforms supporting circular convolution over a commutative ring with identity},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {36},
year = {1995},
pages = {395-400},
zbl = {0860.15003},
mrnumber = {1357538},
language = {en},
url = {http://dml.mathdoc.fr/item/118765}
}
Nessibi, Mohamed Mounir. Linear transforms supporting circular convolution over a commutative ring with identity. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 395-400. http://gdmltest.u-ga.fr/item/118765/
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