On a nonlinear Peetre's theorem in full Colombeau algebras
Commentationes Mathematicae Universitatis Carolinae (2017)
- Volume: 58, Issue: 1, page 69-77
- ISSN: 0010-2628
Access Full Article
top
Abstract
topHow to cite
topNigsch, E. A.. "On a nonlinear Peetre's theorem in full Colombeau algebras." Commentationes Mathematicae Universitatis Carolinae 58.1 (2017): 69-77. <http://eudml.org/doc/287886>.
@article{Nigsch2017,
abstract = {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.},
author = {Nigsch, E. A.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {nonlinear Peetre's theorem; local function; Colombeau algebra},
language = {eng},
number = {1},
pages = {69-77},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On a nonlinear Peetre's theorem in full Colombeau algebras},
url = {http://eudml.org/doc/287886},
volume = {58},
year = {2017},
}
TY - JOUR
AU - Nigsch, E. A.
TI - On a nonlinear Peetre's theorem in full Colombeau algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 1
SP - 69
EP - 77
AB - 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.
LA - eng
KW - nonlinear Peetre's theorem; local function; Colombeau algebra
UR - http://eudml.org/doc/287886
ER -
References
top- Biagioni H.A., A Nonlinear Theory of Generalized Functions, 2nd ed., Springer, Berlin, 1990. Zbl0694.46032MR1049623
- Colombeau J.F., New Generalized Functions and Multiplication of Distributions, North-Holland Mathematics Studies, 84, North-Holland Publishing Co., Amsterdam, 1984. Zbl0761.46021MR0738781
- Colombeau J.F., Elementary Introduction to New Generalized Functions, North-Holland Mathematics Studies, 113, North-Holland Publishing Co., Amsterdam, 1985. Zbl0584.46024MR0808961
- Grosser M., Farkas E., Kunzinger M., Steinbauer R., On the foundations of nonlinear generalized functions I, II, Memoirs. Amer. Math. Soc. 729 (2001). Zbl0985.46026
- 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. Zbl0998.46015MR1883263
- Grosser M., Kunzinger M., Steinbauer R., Vickers J.A., 10.1006/aima.2001.2018, Adv. Math. 166 (2002), no. 1, 50–72. Zbl0995.46054MR1882858DOI10.1006/aima.2001.2018
- Kriegl A., Michor P.W., 10.1090/surv/053, Mathematical Surveys and Monographs, 53, American Mathematical Society, Providence, RI, 1997. Zbl0889.58001MR1471480DOI10.1090/surv/053
- Narasimhan R., Analysis on Real and Complex Manifolds, North-Holland Mathematical Library, 35, reprint of the 1973 edition, North-Holland Publishing Co., Amsterdam, 1985. Zbl0583.58001MR0832683
- Nigsch E.A., 10.1016/j.jmaa.2014.07.014, J. Math. Anal. Appl. 421 (2015), no. 1, 415–435. Zbl1314.46055MR3250487DOI10.1016/j.jmaa.2014.07.014
- Nigsch E.A., 10.1016/j.jmaa.2016.03.022, J. Math. Anal. Appl. 440 (2016), 183–219. MR3479595DOI10.1016/j.jmaa.2016.03.022
- Oberguggenberger M., Multiplication of Distributions and Applications to Partial Differential Equations, Pitman Research Notes in Mathematics, 259, Longman, Harlow, U.K., 1992. Zbl0818.46036MR1187755
- Schwartz L., Sur l'impossibilité de la multiplication des distributions, Comptes Rendus de l'Académie des Sciences 239 (1954), 847–848. Zbl0056.10602MR0064324
- Slovák J., 10.1007/BF00054575, Ann. Global Anal. Geom. 6 (1988), no. 3, 273–283. Zbl0636.58042MR0982996DOI10.1007/BF00054575
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.