| Title:
|
A note on the convolution theorem for the Fourier transform (English) |
| Author:
|
Kahane, Charles S. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
199-207 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
convolution |
| Keyword:
|
Fourier transform |
| MSC:
|
39B22 |
| MSC:
|
42A38 |
| MSC:
|
47B33 |
| MSC:
|
47B38 |
| idZBL:
|
Zbl 1224.42016 |
| idMR:
|
MR2782768 |
| DOI:
|
10.1007/s10587-011-0006-1 |
| . |
| Date available:
|
2011-05-23T12:41:09Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141527 |
| . |
| Reference:
|
[1] Járai, A.: Measurable solutions of functional equations satisfied almost everywhere.Math. Pannon. 10 (1999), 103-110. MR 1678112 |
| Reference:
|
[2] Krantz, S.: A Panorama of Harmonic Analysis, The Carus Mathematical Monographs.Number 27, The Mathematical Association of America, Washington D.C. (1999). MR 1710388 |
| Reference:
|
[3] Rudin, W.: Real and Complex Analysis.McGraw-Hill, New York, 1st edition (1966). Zbl 0142.01701, MR 0210528 |
| Reference:
|
[4] Stein, E. M., Shakarchi, R.: Real Analysis.Princeton University Press, Princeton, New Jersey (2005). Zbl 1081.28001, MR 2129625 |
| . |
