Locally convex topological algebras of generalized functions: Compactness and nuclearity in a nonlinear context
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- by J. Aragona, S. O. Juriaans and J. F. Colombeau PDF
- Trans. Amer. Math. Soc. 367 (2015), 5399-5414 Request permission
Abstract:
In this paper we introduce Hausdorff locally convex algebra topologies on subalgebras of the whole algebra of nonlinear generalized functions. These topologies are strong duals of Fréchet-Schwartz space topologies and even strong duals of nuclear Fréchet space topologies. In particular, any bounded set is relatively compact and one benefits from all deep properties of nuclearity. These algebras of generalized functions contain most of the classical irregular functions and distributions. They are obtained by replacing the mathematical tool of $\mathcal {C}^\infty$ functions in the original version of nonlinear generalized functions by the far more evolved tool of holomorphic functions. This paper continues the nonlinear theory of generalized functions in which such locally convex topological properties were strongly lacking up to now.References
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Additional Information
- J. Aragona
- Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Sao Paulo-CP 66281, Brazil
- Email: aragona@ime.usp.br
- S. O. Juriaans
- Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Sao Paulo-CP 66281, Brazil
- Email: ostanley@usp.br
- J. F. Colombeau
- Affiliation: Institut Fourier, Université de Grenoble, 38042 Grenoble Cedex 09, France
- Email: jf.colombeau@wanadoo.fr
- Received by editor(s): December 25, 2012
- Received by editor(s) in revised form: May 27, 2013
- Published electronically: March 26, 2015
- Additional Notes: The work of the third author was done under the financial support of FAPESP, processo 2011/12532-1, and thanks to the hospitality of the IME-USP. The third author is the corresponding author
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 367 (2015), 5399-5414
- MSC (2010): Primary 46F30, 46F10
- DOI: https://doi.org/10.1090/S0002-9947-2015-06213-8
- MathSciNet review: 3347177
Dedicated: Dedicated to the memory of Leopoldo Nachbin