An intrinsic definition of the Colombeau generalized functions

Jiří Jelínek

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 1, page 71-95
  • ISSN: 0010-2628

Abstract

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A slight modification of the definition of the Colombeau generalized functions allows to have a canonical embedding of the space of the distributions into the space of the generalized functions on a 𝒞 ∞ manifold. The previous attempt in [5] is corrected, several equivalent definitions are presented.

How to cite

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Jelínek, Jiří. "An intrinsic definition of the Colombeau generalized functions." Commentationes Mathematicae Universitatis Carolinae 40.1 (1999): 71-95. <http://eudml.org/doc/248380>.

@article{Jelínek1999,
abstract = {A slight modification of the definition of the Colombeau generalized functions allows to have a canonical embedding of the space of the distributions into the space of the generalized functions on a $\mathcal \{C\}^\infty $ manifold. The previous attempt in [5] is corrected, several equivalent definitions are presented.},
author = {Jelínek, Jiří},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Colombeau generalized function; distribution; canonical embedding; manifold; Colombeau generalized function; distribution; canonical embedding; manifold},
language = {eng},
number = {1},
pages = {71-95},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {An intrinsic definition of the Colombeau generalized functions},
url = {http://eudml.org/doc/248380},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Jelínek, Jiří
TI - An intrinsic definition of the Colombeau generalized functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 1
SP - 71
EP - 95
AB - A slight modification of the definition of the Colombeau generalized functions allows to have a canonical embedding of the space of the distributions into the space of the generalized functions on a $\mathcal {C}^\infty $ manifold. The previous attempt in [5] is corrected, several equivalent definitions are presented.
LA - eng
KW - Colombeau generalized function; distribution; canonical embedding; manifold; Colombeau generalized function; distribution; canonical embedding; manifold
UR - http://eudml.org/doc/248380
ER -

References

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  12. Pietsch A., Nukleare Lokalkonvexe Räume, Akademie-Verlag, Berlin. Zbl0184.14602MR0181888
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  14. Robertson + Robertson, Topological Vector Spaces, Cambridge Univ. Press, Cambridge (1964). (1964) MR0162118
  15. Roever J.W., Damsma M., Colombeau algebras on a 𝒞 ∞ -manifold, Indag. Math. N.S. 2.3 (1991), 341-358. (1991) MR1149687
  16. Schwartz L., Théorie des Distributions, Paris, Hermann (1966). (1966) Zbl0149.09501MR0209834
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