Equality of two diffeomorphism invariant Colombeau algebras

Jiří Jelínek

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 4, page 633-662
  • ISSN: 0010-2628

Abstract

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The two diffeomorphism invariant algebras introduced in Grosser M., Farkas E., Kunziger M., Steinbauer R., On the foundations of nonlinear generalized functions I, II, Mem. Amer. Math. Soc. 153 (2001), no. 729, 93 pp., are identical.

How to cite

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Jelínek, Jiří. "Equality of two diffeomorphism invariant Colombeau algebras." Commentationes Mathematicae Universitatis Carolinae 45.4 (2004): 633-662. <http://eudml.org/doc/249364>.

@article{Jelínek2004,
abstract = {The two diffeomorphism invariant algebras introduced in Grosser M., Farkas E., Kunziger M., Steinbauer R., On the foundations of nonlinear generalized functions I, II, Mem. Amer. Math. Soc. 153 (2001), no. 729, 93 pp., are identical.},
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 = {633-662},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Equality of two diffeomorphism invariant Colombeau algebras},
url = {http://eudml.org/doc/249364},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Jelínek, Jiří
TI - Equality 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 - 633
EP - 662
AB - The two diffeomorphism invariant algebras introduced in Grosser M., Farkas E., Kunziger M., Steinbauer R., On the foundations of nonlinear generalized functions I, II, Mem. Amer. Math. Soc. 153 (2001), no. 729, 93 pp., are identical.
LA - eng
KW - Colombeau algebra of generalized functions; representative; diffeomorphism invariance; Colombeau algebra of generalized functions
UR - http://eudml.org/doc/249364
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. Deville R., Godefroy G., Zizler V., Smoothness and Renormings in Banach Spaces, John Wiley, New York, 1993. Zbl0782.46019MR1211634
  6. 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
  7. 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
  8. Jelínek J., An intrinsic definition of the Colombeau generalized functions, Comment. Math. Univ. Carolinae 40.1 (1999), 71-95. (1999) MR1715203
  9. Jelínek J., On introduction of two diffeomorphism invariant Colombeau algebras, Comment. Math. Univ. Carolinae 45.4 (2004), 615-632. (2004) Zbl1103.46020MR2103080
  10. Kuratowski, Topology, Academic Press, New York-London; PWN, Warsaw, 1966. Zbl0849.01044
  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). (1966) Zbl0149.09501MR0209834
  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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