| Title:
|
Solving singular convolution equations using the inverse fast Fourier transform (English) |
| Author:
|
Krajník, Eduard |
| Author:
|
Montesinos, Vincente |
| Author:
|
Zizler, Peter |
| Author:
|
Zizler, Václav |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
57 |
| Issue:
|
5 |
| Year:
|
2012 |
| Pages:
|
543-550 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The inverse Fast Fourier Transform is a common procedure to solve a convolution equation provided the transfer function has no zeros on the unit circle. In our paper we generalize this method to the case of a singular convolution equation and prove that if the transfer function is a trigonometric polynomial with simple zeros on the unit circle, then this method can be extended. (English) |
| Keyword:
|
singular convolution equations |
| Keyword:
|
fast Fourier transform |
| Keyword:
|
tempered distribution |
| Keyword:
|
polynomial transfer functions |
| Keyword:
|
simple zeros |
| MSC:
|
42A85 |
| MSC:
|
65R10 |
| MSC:
|
65T50 |
| idZBL:
|
Zbl 1265.42020 |
| idMR:
|
MR2984619 |
| DOI:
|
10.1007/s10492-012-0032-9 |
| . |
| Date available:
|
2012-08-19T22:10:40Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142916 |
| . |
| Reference:
|
[1] Babuška, I.: The Fourier transform in the theory of difference equations and its applications.Arch. Mech. 11 (1959), 349-381. Zbl 0092.12201, MR 0115030 |
| Reference:
|
[2] Beals, R.: Advanced Mathematical Analysis. GTM 12.Springer New York-Heidelberg-Berlin (1973). MR 0530403 |
| Reference:
|
[3] Fisher, B.: The product of distributions.Q. J. Math. 22 (1971), 291-298. Zbl 0213.13104, MR 0287308, 10.1093/qmath/22.2.291 |
| Reference:
|
[4] Jarchow, H.: Locally Convex Spaces.B. G. Teubner Stuttgart (1981). Zbl 0466.46001, MR 0632257 |
| Reference:
|
[5] Rudin, W.: Functional Analysis.McGraw-Hill New York (1973). Zbl 0253.46001, MR 0365062 |
| Reference:
|
[6] Vitásek, E.: Periodic distributions and discrete Fourier transforms.Pokroky mat., fyz. astronom. 54 (2009), 137-144 Czech. |
| Reference:
|
[7] Walter, G. G.: Wavelets and Other Orthogonal Systems with Applications.CRC Press Boca Raton (1994). Zbl 0866.42022, MR 1300204 |
| Reference:
|
[8] Walsh, J. L., Sewell, W. E.: Note on degree of approximation to an integral by Riemann sums.Am. Math. Monthly 44 (1937), 155-160. Zbl 0016.29901, MR 1523881, 10.2307/2301660 |
| . |
