| Title:
|
On introduction of two diffeomorphism invariant Colombeau algebras (English) |
| Author:
|
Jelínek, Jiří |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
615-632 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Equivalent definitions of two diffeomorphism invariant Colombeau algebras introduced in [7] and [5] (Grosser et al.) are listed and some new equivalent definitions are presented. The paper can be treated as tools for proving in [8] the equality of both algebras. (English) |
| Keyword:
|
Colombeau algebra of generalized functions |
| Keyword:
|
representative |
| Keyword:
|
diffeomorphism invariance |
| MSC:
|
46F05 |
| MSC:
|
46F30 |
| idZBL:
|
Zbl 1103.46020 |
| idMR:
|
MR2103080 |
| . |
| Date available:
|
2009-05-05T16:48:03Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119490 |
| . |
| Reference:
|
[1] Colombeau J.F.: Differential Calculus and Holomorphy.North Holland Math. Studies 64 (1982). Zbl 0506.46001, MR 0671252 |
| Reference:
|
[2] Colombeau J.F.: New Generalized Functions and Multiplication of Distributions.North Holland Math. Studies 84 (1984). Zbl 0532.46019, MR 0738781 |
| Reference:
|
[3] Colombeau J.F.: Elementary Introduction to New Generalized Functions.North Holland Math. Studies 113 (1985). Zbl 0584.46024, MR 0808961 |
| Reference:
|
[4] 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:
|
[5] Grosser M., Farkas E., Kunziger M., Steinbauer R.: On the foundations of nonlinear generalized functions I, II.Mem. Amer. Math. Soc. 153 729 (2001), 93pp. MR 1848157 |
| Reference:
|
[6] Grosser M., Kunziger M., Steinbauer R., Vickers J.: A global theory of algebras of generalized functions.Adv. Math. 166 1 (2002), 50-72. MR 1882858 |
| Reference:
|
[7] Jelínek J.: An intrinsic definition of the Colombeau generalized functions.Comment. Math. Univ. Carolinae 40.1 (1999), 71-95. MR 1715203 |
| Reference:
|
[8] Jelínek J.: Equality of two diffeomorphism invariant Colombeau algebras.Comment. Math. Univ. Carolinae 45.4 (2004), 633-662. Zbl 1103.46021, MR 2103081 |
| Reference:
|
[9] Kriegl A., Michor P.W.: The Convenient Setting of Global Analysis.Math. Surveys and Monographs 53, Amer. Math. Soc., Providence, RI (1997). Zbl 0889.58001, MR 1471480 |
| Reference:
|
[10] Pietsch A.: Nukleare Lokalkonvexe Räume.Akademie-Verlag, Berlin, 1965. Zbl 0184.14602, MR 0181888 |
| Reference:
|
[11] Robertson A.P., Robertson W.J.: Topological Vector Spaces.Cambridge Univ. Press, New York, 1964. Zbl 0423.46001, MR 0162118 |
| Reference:
|
[12] Schwartz L.: Théorie des Distributions.Hermann, Paris, 1966. Zbl 0962.46025, MR 0209834 |
| Reference:
|
[13] Yamamuro S.: Differential Calculus in Topological Linear Spaces.Lecture Notes in Math. 374, Springer, Berlin-New York, 1974. Zbl 0336.58006, MR 0488118 |
| . |
