| Title:
|
On a nonlinear Peetre's theorem in full Colombeau algebras (English) |
| Author:
|
Nigsch, E. A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
58 |
| Issue:
|
1 |
| Year:
|
2017 |
| Pages:
|
69-77 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We adapt a nonlinear version of Peetre's theorem on local operators in order to investigate representatives of nonlinear generalized functions occurring in the theory of full Colombeau algebras. (English) |
| Keyword:
|
nonlinear Peetre's theorem |
| Keyword:
|
local function |
| Keyword:
|
Colombeau algebra |
| MSC:
|
46F30 |
| idZBL:
|
Zbl 06736744 |
| idMR:
|
MR3631681 |
| DOI:
|
10.14712/1213-7243.2015.197 |
| . |
| Date available:
|
2017-03-12T16:38:37Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146028 |
| . |
| Reference:
|
[1] Biagioni H.A.: A Nonlinear Theory of Generalized Functions.2nd ed., Springer, Berlin, 1990. Zbl 0694.46032, MR 1049623 |
| Reference:
|
[2] Colombeau J.F.: New Generalized Functions and Multiplication of Distributions.North-Holland Mathematics Studies, 84, North-Holland Publishing Co., Amsterdam, 1984. Zbl 0761.46021, MR 0738781 |
| Reference:
|
[3] Colombeau J.F.: Elementary Introduction to New Generalized Functions.North-Holland Mathematics Studies, 113, North-Holland Publishing Co., Amsterdam, 1985. Zbl 0584.46024, MR 0808961 |
| Reference:
|
[4] Grosser M., Farkas E., Kunzinger M., Steinbauer R.: On the foundations of nonlinear generalized functions I, II.Memoirs. Amer. Math. Soc. 729 (2001). Zbl 0985.46026 |
| Reference:
|
[5] Grosser M., Kunzinger M., Oberguggenberger M., Steinbauer R.: Geometric Theory of Generalized Functions with Applications to General Relativity.Mathematics and its Applications, 537, Kluwer Academic Publishers, Dordrecht, 2001. Zbl 0998.46015, MR 1883263 |
| Reference:
|
[6] Grosser M., Kunzinger M., Steinbauer R., Vickers J.A.: A global theory of algebras of generalized functions.Adv. Math. 166 (2002), no. 1, 50–72. Zbl 0995.46054, MR 1882858, 10.1006/aima.2001.2018 |
| Reference:
|
[7] Kriegl A., Michor P.W.: The Convenient Setting of Global Analysis.Mathematical Surveys and Monographs, 53, American Mathematical Society, Providence, RI, 1997. Zbl 0889.58001, MR 1471480, 10.1090/surv/053 |
| Reference:
|
[8] Narasimhan R.: Analysis on Real and Complex Manifolds.North-Holland Mathematical Library, 35, reprint of the 1973 edition, North-Holland Publishing Co., Amsterdam, 1985. Zbl 0583.58001, MR 0832683 |
| Reference:
|
[9] Nigsch E.A.: The functional analytic foundation of Colombeau algebras.J. Math. Anal. Appl. 421 (2015), no. 1, 415–435. Zbl 1314.46055, MR 3250487, 10.1016/j.jmaa.2014.07.014 |
| Reference:
|
[10] Nigsch E.A.: Nonlinear generalized sections of vector bundles.J. Math. Anal. Appl. 440 (2016), 183–219. MR 3479595, 10.1016/j.jmaa.2016.03.022 |
| Reference:
|
[11] Oberguggenberger M.: Multiplication of Distributions and Applications to Partial Differential Equations.Pitman Research Notes in Mathematics, 259, Longman, Harlow, U.K., 1992. Zbl 0818.46036, MR 1187755 |
| Reference:
|
[12] Schwartz L.: Sur l'impossibilité de la multiplication des distributions.Comptes Rendus de l'Académie des Sciences 239 (1954), 847–848. Zbl 0056.10602, MR 0064324 |
| Reference:
|
[13] Slovák J.: Peetre theorem for nonlinear operators.Ann. Global Anal. Geom. 6 (1988), no. 3, 273–283. Zbl 0636.58042, MR 0982996, 10.1007/BF00054575 |
| . |
