| Title:
|
A Tauberian theorem for distributions (English) |
| Author:
|
Čížek, Jiří |
| Author:
|
Jelínek, Jiří |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
479-488 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The well-known general Tauberian theorem of N. Wiener is formulated and proved for distributions in the place of functions and its Ganelius' formulation is corrected. Some changes of assumptions of this theorem are discussed, too. (English) |
| Keyword:
|
Tauberian theorem |
| Keyword:
|
distribution |
| Keyword:
|
convolution |
| Keyword:
|
Fourier transform |
| MSC:
|
40E05 |
| MSC:
|
42A38 |
| MSC:
|
44A35 |
| MSC:
|
46F05 |
| MSC:
|
46F10 |
| idZBL:
|
Zbl 0881.40006 |
| idMR:
|
MR1426912 |
| . |
| Date available:
|
2009-01-08T18:25:25Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118854 |
| . |
| Reference:
|
[1] Dierolf P., Voigt J.: Convolutions and $S'$-convolutions of distributions.Collect. Math. 29 (1978), 185-196. MR 0565276 |
| Reference:
|
[2] Ganelius T.H.: Tauberian Remainder Theorems.Lecture Notes in Math. 232 (1971), 75. Zbl 0222.40001, MR 0499898 |
| Reference:
|
[3] Grothendieck A.: Produits Tensoriels topologiques et espaces nuclaires.Memoirs of the AMS 16 (1966), 196+140. MR 0075539 |
| Reference:
|
[4] Hardy G.H.: Divergent Series.Oxford (1949). Zbl 0032.05801, MR 0030620 |
| Reference:
|
[5] Horvth J.: Topological Vector Spaces and Distributions.Addison-Wesley Publishing Company (1966), 449. |
| Reference:
|
[6] Hirata, Ogata: On the exchange formula for distributions.J. Sci. Hiroshima Univ. Ser. A 22 (1958), 147-152. MR 0110014 |
| Reference:
|
[7] Itano M.: On the theory of multiplicative products of distributions.J. Sci. Hiroshima Univ. Ser. A-I 30 (1966), 151-181. MR 0209835 |
| Reference:
|
[8] Kamiński A.: Convolution, product and Fourier transform of distributions.Stud. Math 74 (1982), 83-96. MR 0675434 |
| Reference:
|
[9] Oberguggenberger M.: Multiplication of Distributions and Applications to Partial Differential Equations.Institut für Mathematik und Geometrie, Universität Innsbruck, Austria, 1992, p. 312. Zbl 0818.46036, MR 1187755 |
| Reference:
|
[10] Pilipović S., Stanković B.: Wiener Tauberian theorems for distributions.J. London Math. Society, Second Series 47.3 (1993), 507-515. MR 1214912 |
| Reference:
|
[11] Shiraishi R.: On the definition of convolutions for distributions.J. Sci. Hiroshima Univ. Ser. A 23.1 (April 1959), 19-32. Zbl 0091.28601, MR 0114122 |
| Reference:
|
[12] Schwartz L.: Theorie des distributions I, II.Herman, Paris (1957). MR 0209834 |
| Reference:
|
[13] Wiener N.: Tauberian theorems.Ann. of Math. (2) 33 (1932), 1-100. Zbl 0005.25003, MR 1503035 |
| . |
