| Title:
|
Colombeau product of currents (English) |
| Author:
|
Jelínek, Jiří |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
437-462 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Colombeau product of de Rham's currents coincides with generalized Itano one. Sufficient conditions are found under which it is diffeomorphism invariant. (English) |
| Keyword:
|
de Rham's current |
| Keyword:
|
full Colombeau algebra |
| MSC:
|
46F05 |
| MSC:
|
46F10 |
| MSC:
|
46F30 |
| MSC:
|
58A25 |
| idZBL:
|
Zbl 1123.46025 |
| idMR:
|
MR2174523 |
| . |
| Date available:
|
2009-05-05T16:52:19Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119539 |
| . |
| Reference:
|
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| Reference:
|
[2] Colombeau J.F.: Differential Calculus and Holomorphy.North Holland Math. Studies 64 (1982). Zbl 0506.46001, MR 0671252 |
| Reference:
|
[3] Colombeau J.F.: New Generalized Functions and Multiplication of Distributions.North Holland Math. Studies 84 (1984). Zbl 0532.46019, MR 0738781 |
| Reference:
|
[4] Colombeau J.F.: Elementary Introduction to New Generalized Functions.North Holland Math. Studies 113 (1985). Zbl 0584.46024, MR 0808961 |
| Reference:
|
[5] Colombeau J.F., Meril A.: Generalized Functions and Multiplication of Distributions on C$^\infty$ Manifolds.J. Math. Anal. Appl. 186 (1994), 357-364. MR 1292997 |
| Reference:
|
[6] Grosser M., Farkas E., Kunzinger M., Steinbauer R.: On the foundations of nonlinear generalized functions I, II.Mem. Amer. Math. Soc. 153 729 (2001), 93 pp. Zbl 0985.46026, MR 1848157 |
| Reference:
|
[7] Grosser M., Kunzinger M., Steinbauer R., Vickers J.A.: A global theory of algebras of generalized functions.Adv. Math. 166 (2002), 50-72. Zbl 0995.46054, MR 1882858 |
| Reference:
|
[8] Grosser M., Kunzinger M., Oberguggenberger M., Steinbauer R.: Geometric Theory of Generalized Functions with Applications to General Relativity.Kluwer Academic Publishers, Dordrecht (2001). Zbl 0998.46015, MR 1883263 |
| Reference:
|
[9] Itano M.: On fixations and reciprocal images of currents.J. Sci. Hiroshima Univ. Ser. A-1 31 (1967), 173-190. Zbl 0165.47503, MR 0231195 |
| Reference:
|
[10] Jelínek J.: Characterization of the Colombeau product of distributions.Comment. Math. Univ. Carolinae 27.2 (1986), 377-394. MR 0857556 |
| Reference:
|
[11] Jelínek J.: An intrinsic definition of the Colombeau generalized functions.Comment. Math. Univ. Carolinae 40.1 (1999), 71-95. MR 1715203 |
| Reference:
|
[12] Jelínek J.: On introduction of two diffeomorphism invariant Colombeau algebras.Comment. Math. Univ. Carolinae 45.4 (2004), 615-632. Zbl 1103.46020, MR 2103080 |
| Reference:
|
[13] Jelínek J.: Equality of two diffeomorphism invariant Colombeau algebras.Comment. Math. Univ. Carolinae 45.4 (2004), 633-662. Zbl 1103.46021, MR 2103081 |
| Reference:
|
[14] Lojasiewicz S.: Sur la fixation des variables dans une distribuion.Studia Math. 17 (1958), 1-64. MR 0107167 |
| Reference:
|
[15] Schwartz L.: Théorie des Distributions.Hermann, Paris (1966). Zbl 0149.09501, MR 0209834 |
| . |
