| Title:
|
Results on Colombeau product of distributions (English) |
| Author:
|
Damyanov, Blagovest |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
4 |
| Year:
|
1997 |
| Pages:
|
627-634 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The differential $\Bbb C$-algebra $\Cal G(\Bbb R^m)$ of generalized functions of J.-F. Colombeau contains the space $\Cal D'(\Bbb R^m)$ of Schwartz distributions as a $\Bbb C$-vector subspace and has a notion of `association' that is a faithful generalization of the weak equality in $\Cal D'(\Bbb R^m)$. This is particularly useful for evaluation of certain products of distributions, as they are embedded in $\Cal G(\Bbb R^m)$, in terms of distributions again. In this paper we propose some results of that kind for the products of the widely used distributions $x_{\pm}^a$ and $\delta ^{(p)}(x)$, with $x$ in $\Bbb R^m$, that have coinciding singular supports. These results, when restricted to dimension one, are also easily transformed into the setting of regularized model products in the classical distribution theory. (English) |
| Keyword:
|
multiplication of Schwartz distributions |
| Keyword:
|
Colombeau generalized functions |
| MSC:
|
46F10 |
| idZBL:
|
Zbl 0937.46030 |
| idMR:
|
MR1601668 |
| . |
| Date available:
|
2009-01-08T18:36:54Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118961 |
| . |
| Reference:
|
[1] Colombeau J.-F.: New Generalized Functions and Multiplication of Distributions.North Holland Math. Studies 84, Amsterdam, 1984. Zbl 0761.46021, MR 0738781 |
| Reference:
|
[2] Fisher B.: The product of distributions.Quart. J. Oxford 22 (1971), 291-298. Zbl 0213.13104, MR 0287308 |
| Reference:
|
[3] Fisher B.: The divergent distribution product $x_+^\lambda x_-^\mu$.Sem. Mat. Barcelona 27 (1976), 3-10. MR 0425606 |
| Reference:
|
[4] Friedlander F.G.: Introduction to the Theory of Distributions.Cambridge Univ. Press, Cambridge, 1982. Zbl 0499.46020, MR 0779092 |
| Reference:
|
[5] Jelínek J.: Characterization of the Colombeau product of distributions.Comment. Math. Univ. Carolinae 27 (1986), 377-394. MR 0857556 |
| Reference:
|
[6] Korn G.A., Korn T.M.: Mathematical Handbook.McGraw-Hill Book Company, New York, 1968. Zbl 0535.00032, MR 0220560 |
| Reference:
|
[7] Oberguggenberger M.: Multiplication of Distributions and Applications to Partial Differential Equations.Longman, Essex, 1992. Zbl 0818.46036, MR 1187755 |
| . |
