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Title: On introduction of two diffeomorphism invariant Colombeau algebras (English)
Author: Jelínek, Jiří
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 45
Issue: 4
Year: 2004
Pages: 615-632
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Category: math
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Summary: 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. (English)
Keyword: Colombeau algebra of generalized functions
Keyword: representative
Keyword: diffeomorphism invariance
MSC: 46F05
MSC: 46F30
idZBL: Zbl 1103.46020
idMR: MR2103080
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Date available: 2009-05-05T16:48:03Z
Last updated: 2012-04-30
Stable URL: http://hdl.handle.net/10338.dmlcz/119490
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Reference: [1] Colombeau J.F.: Differential Calculus and Holomorphy.North Holland Math. Studies 64 (1982). Zbl 0506.46001, MR 0671252
Reference: [2] Colombeau J.F.: New Generalized Functions and Multiplication of Distributions.North Holland Math. Studies 84 (1984). Zbl 0532.46019, MR 0738781
Reference: [3] Colombeau J.F.: Elementary Introduction to New Generalized Functions.North Holland Math. Studies 113 (1985). Zbl 0584.46024, MR 0808961
Reference: [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
Reference: [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. MR 1848157
Reference: [6] 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
Reference: [7] Jelínek J.: An intrinsic definition of the Colombeau generalized functions.Comment. Math. Univ. Carolinae 40.1 (1999), 71-95. MR 1715203
Reference: [8] Jelínek J.: Equality of two diffeomorphism invariant Colombeau algebras.Comment. Math. Univ. Carolinae 45.4 (2004), 633-662. Zbl 1103.46021, MR 2103081
Reference: [9] Kriegl A., Michor P.W.: The Convenient Setting of Global Analysis.Math. Surveys and Monographs 53, Amer. Math. Soc., Providence, RI (1997). Zbl 0889.58001, MR 1471480
Reference: [10] Pietsch A.: Nukleare Lokalkonvexe Räume.Akademie-Verlag, Berlin, 1965. Zbl 0184.14602, MR 0181888
Reference: [11] Robertson A.P., Robertson W.J.: Topological Vector Spaces.Cambridge Univ. Press, New York, 1964. Zbl 0423.46001, MR 0162118
Reference: [12] Schwartz L.: Théorie des Distributions.Hermann, Paris, 1966. Zbl 0962.46025, MR 0209834
Reference: [13] Yamamuro S.: Differential Calculus in Topological Linear Spaces.Lecture Notes in Math. 374, Springer, Berlin-New York, 1974. Zbl 0336.58006, MR 0488118
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