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A nonlinear theory of generalized functions

  • Special issue commemorating the Golden Jubilee of the Institute of Mathematics and Statistics of the University of São Paulo
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Abstract

Generalized Functions are crucial in the development of theories modeling physical reality. Starting with the linear theory, we give a partial account of what is known, focussing on the non-linear theory and some of its more recent achievements.

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Acknowledgements

The second author is very much indebted to Jorge Aragona for introducing him into the subject of Colombeau generalized functions in 1997 and for his collaboration throughout the years following this. His ideas and mathematical precision are the things which will be remembered. He is also indebted to J.F. Colombeau for many valuable teachings and collaborations. It was a privilege to have learned from the creator and masters of the theory.

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Authors and Affiliations

  1. Centro de Ciências Exatas e Naturais, Universidade Federal Rural do Semi-Árido, Mossoró, RN, Brazil

    A. R. G. Garcia & W. M. Rodrigues

  2. IME - Universidade de São Paulo, São Paulo, SP, Brazil

    S. O. Juriaans

  3. Departamento de Matemática, Universidade Federal de Roraima, Boa Vista, RR, Brazil

    J. Oliveira

Authors
  1. A. R. G. Garcia
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  2. S. O. Juriaans
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  3. J. Oliveira
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  4. W. M. Rodrigues
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Corresponding author

Correspondence to S. O. Juriaans.

Additional information

Communicated by Claudio Gorodski.

In honor of Alfredo Jorge Aragona Vallejo (In memoriam).

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Garcia, A.R.G., Juriaans, S.O., Oliveira, J. et al. A nonlinear theory of generalized functions. São Paulo J. Math. Sci. 16, 396–405 (2022). https://doi.org/10.1007/s40863-020-00205-0

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