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Keywords:
Colombeau generalized function; distribution; canonical embedding; manifold
Colombeau generalized function; distribution; canonical embedding; manifold
Summary:
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 \text{$\Cal C^\infty $} manifold. The previous attempt in [5] is corrected, several equivalent definitions are presented.
References:
[1] Biagioni H.A.: A Nonlinear Theory of Generalized Functions. Lecture Notes in Math. 1421, Springer-Verlag (1990). MR 1049623 | Zbl 0694.46032
[2] Colombeau J.F.: Differential Calculus and Holomorphy. North Holland Math. Studies 64 (1982). MR 0671252 | Zbl 0506.46001
[3] Colombeau J.F.: New Generalized Functions and Multiplication of Distributions. North Holland Math. Studies 84 (1984). MR 0738781 | Zbl 0532.46019
[4] Colombeau J.F.: Elementary Introduction to New Generalized Functions. North Holland Math. Studies 113 (1985). MR 0808961 | Zbl 0584.46024
[5] Colombeau J.F., Meril A.: Generalized functions and multiplication of distributions on $\Cal C^\infty $ manifolds. J. Math. Anal. Appl. 186 (1994), 357-364. MR 1292997
[6] Dapić and Pilipović: Microlocal analysis of Colombeau's generalized functions on a manifold. Indag. Math. N.S. 7.3 (1996), 293-309. MR 1621385
[7] Engelking R.: Outline of General Topology. North-Holland Publishing Company, Amsterdam (1968), 388. MR 0230273 | Zbl 0157.53001
[8] Hörmander L.: The Analysis of Linear Partial Differential Operators I, Distribution Theory and Fourier Analysis. ().
[9] Egorov Yu.V.: On the theory of generalized functions (in Russian). Russian Math. Surveys 45.5 (1990), 1-49. MR 1084986
[10] Itano M.: On fixation and reciprocal images of currents. J. Sci. Hiroshima Univ. A-I, 31.2 (1967). MR 0231195
[11] Jelínek J.: Characterization of the Colombeau product of distributions. Comment. Math. Univ. Carolinae 27.2 (1986). MR 0857556
[12] Pietsch A.: Nukleare Lokalkonvexe Räume. Akademie-Verlag, Berlin. MR 0181888 | Zbl 0184.14602
[13] de Rham G.: Variétés Différentiables. Paris, Hermann (1955). Zbl 0065.32401
[14] Robertson + Robertson: Topological Vector Spaces. Cambridge Univ. Press, Cambridge (1964). MR 0162118
[15] Roever J.W., Damsma M.: Colombeau algebras on a $\Cal C^\infty $-manifold. Indag. Math. N.S. 2.3 (1991), 341-358. MR 1149687
[16] Schwartz L.: Théorie des Distributions. Paris, Hermann (1966). MR 0209834 | Zbl 0149.09501
[17] Yamamuro S.: Differential Calculus in Topological Linear Spaces. Lecture Notes in Math. 374, Springer-Verlag (1974). MR 0488118 | Zbl 0276.58001
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