Article
Keywords:
Colombeau algebra of generalized functions; representative; diffeomorphism invariance
Summary:
The two diffeomorphism invariant algebras introduced in Grosser  M., Far\-kas  E., Kunziger  M., Steinbauer  R., {\it On the foundations of nonlinear generalized functions I, II\/}, Mem. Amer. Math. Soc. {\bf 153} (2001), no. 729, 93\,pp., are identical.
References:
                        
[1] Colombeau J.F.: 
Differential Calculus and Holomorphy. North Holland Math. Studies 64 (1982). 
MR 0671252 | 
Zbl 0506.46001[2] Colombeau J.F.: 
New Generalized Functions and Multiplication of Distributions. North Holland Math. Studies 84 (1984). 
MR 0738781 | 
Zbl 0532.46019[3] Colombeau J.F.: 
Elementary Introduction to New Generalized Functions. North Holland Math. Studies 113 (1985). 
MR 0808961 | 
Zbl 0584.46024[4] Colombeau J.F., Meril A.: 
Generalized Functions and Multiplication of Distributions on C$^\infty$ Manifolds. J. Math. Anal. Appl. 186 (1994), 357-364. 
MR 1292997[5] Deville R., Godefroy G., Zizler V.: 
Smoothness and Renormings in Banach Spaces. John Wiley, New York, 1993. 
MR 1211634 | 
Zbl 0782.46019[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. 
MR 1848157[7] Grosser M., Kunziger M., Steinbauer R., Vickers J.: 
A global theory of algebras of generalized functions. Adv. Math. 166 1 (2002), 50-72. 
MR 1882858[8] Jelínek J.: 
An intrinsic definition of the Colombeau generalized functions. Comment. Math. Univ. Carolinae 40.1 (1999), 71-95. 
MR 1715203[9] Jelínek J.: 
On introduction of two diffeomorphism invariant Colombeau algebras. Comment. Math. Univ. Carolinae 45.4 (2004), 615-632. 
MR 2103080 | 
Zbl 1103.46020[10] Kuratowski: 
Topology. Academic Press, New York-London; PWN, Warsaw, 1966. 
Zbl 0849.01044[11] Robertson A.P., Robertson W.J.: 
Topological Vector Spaces. Cambridge Univ. Press, New York, 1964. 
MR 0162118 | 
Zbl 0423.46001[13] Yamamuro S.: 
Differential Calculus in Topological Linear Spaces. Lecture Notes in Math. 374, Springer, Berlin-New York, 1974. 
MR 0488118 | 
Zbl 0336.58006