On introduction of two diffeomorphism invariant Colombeau algebras

Jiří Jelínek

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 4, page 615-632
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Jelínek, Jiří. "On introduction of two diffeomorphism invariant Colombeau algebras." Commentationes Mathematicae Universitatis Carolinae 45.4 (2004): 615-632. <http://eudml.org/doc/249346>.

@article{Jelínek2004,
abstract = {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.},
author = {Jelínek, Jiří},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Colombeau algebra of generalized functions; representative; diffeomorphism invariance; Colombeau algebra of generalized functions},
language = {eng},
number = {4},
pages = {615-632},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On introduction of two diffeomorphism invariant Colombeau algebras},
url = {http://eudml.org/doc/249346},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Jelínek, Jiří
TI - On introduction of two diffeomorphism invariant Colombeau algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 4
SP - 615
EP - 632
AB - 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.
LA - eng
KW - Colombeau algebra of generalized functions; representative; diffeomorphism invariance; Colombeau algebra of generalized functions
UR - http://eudml.org/doc/249346
ER -

References

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  1. Colombeau J.F., Differential Calculus and Holomorphy, North Holland Math. Studies 64 (1982). (1982) Zbl0506.46001MR0671252
  2. Colombeau J.F., New Generalized Functions and Multiplication of Distributions, North Holland Math. Studies 84 (1984). (1984) Zbl0532.46019MR0738781
  3. Colombeau J.F., Elementary Introduction to New Generalized Functions, North Holland Math. Studies 113 (1985). (1985) Zbl0584.46024MR0808961
  4. Colombeau J.F., Meril A., Generalized functions and multiplication of distributions on C ∞ manifolds, J. Math. Anal. Appl. 186 (1994), 357-364. (1994) MR1292997
  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. (2001) MR1848157
  6. Grosser M., Kunziger M., Steinbauer R., Vickers J., A global theory of algebras of generalized functions, Adv. Math. 166 1 (2002), 50-72. (2002) MR1882858
  7. Jelínek J., An intrinsic definition of the Colombeau generalized functions, Comment. Math. Univ. Carolinae 40.1 (1999), 71-95. (1999) MR1715203
  8. Jelínek J., Equality of two diffeomorphism invariant Colombeau algebras, Comment. Math. Univ. Carolinae 45.4 (2004), 633-662. (2004) Zbl1103.46021MR2103081
  9. Kriegl A., Michor P.W., The Convenient Setting of Global Analysis, Math. Surveys and Monographs 53, Amer. Math. Soc., Providence, RI (1997). (1997) Zbl0889.58001MR1471480
  10. Pietsch A., Nukleare Lokalkonvexe Räume, Akademie-Verlag, Berlin, 1965. Zbl0184.14602MR0181888
  11. Robertson A.P., Robertson W.J., Topological Vector Spaces, Cambridge Univ. Press, New York, 1964. Zbl0423.46001MR0162118
  12. Schwartz L., Théorie des Distributions, Hermann, Paris, 1966. Zbl0962.46025MR0209834
  13. Yamamuro S., Differential Calculus in Topological Linear Spaces, Lecture Notes in Math. 374, Springer, Berlin-New York, 1974. Zbl0336.58006MR0488118

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