| Title:
|
Linear transforms supporting circular convolution over a commutative ring with identity (English) |
| Author:
|
Nessibi, M. M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
2 |
| Year:
|
1995 |
| Pages:
|
395-400 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $x,y \in \operatorname R^{\operatorname N}$. (English) |
| Keyword:
|
circular convolution property |
| MSC:
|
13B10 |
| MSC:
|
15A04 |
| MSC:
|
15A33 |
| MSC:
|
65T50 |
| idZBL:
|
Zbl 0860.15003 |
| idMR:
|
MR1357538 |
| . |
| Date available:
|
2009-01-08T18:18:44Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118765 |
| . |
| Reference:
|
[1] Cikánek P.: SCC matice nad komutativnim okruhem.PhD-Thesis, Section 5, pp. 63-81, Brno, 1992. |
| Reference:
|
[2] Hasse H.: Number Theory.Springer-Verlag, Berlin-Heidelberg-New York, 1980. Zbl 0991.11001, MR 0562104 |
| Reference:
|
[3] Skula L.: Linear transforms and convolution.Math. Slovaca 37:1 (1987), 9-30. Zbl 0622.65143, MR 0899012 |
| Reference:
|
[4] Skula L.: Linear transforms supporting circular convolution on residue class rings.Math. Slovaca 39:4 (1989), 377-390. Zbl 0778.11073, MR 1094761 |
| Reference:
|
[5] Nussbaumer H.T.: Fast Fourier transform and convolution algorithms.Springer-Verlag, Berlin-Heidelberg-New York, 1981. Zbl 0599.65098, MR 0606376 |
| Reference:
|
[6] Zarisky O., Samuel P.: Commutative Algebra.Vol. 1, 1958, D. van Nostrand, Inc., Princeton, New Jersey, London. |
| . |
