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Colombeau Generalized Functions and Stochastic Analysis

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Stochastic Analysis and Applications in Physics

Part of the book series: NATO ASI Series ((ASIC,volume 449))

Abstract

The class of Colombeau generalized functions has been introduced in the early eightees. A good pedagogical survey about this class and its related calculus can be found in [12]. Recently [13] has presented the state of the art on the actual theory and it has developed some numerical analysis applications. For Colombeau general theory, the reader can also consult [9], [30], [34] and references therein. The purpose was to treat non—linear problems which naturally involve Schwartz distributions. Several examples come out from quantum field theory, see [16], [43]; there, the possibility of defining a good multiplication and non—linear operation for distributions is fundamental. In [45], also some connections with non—standard analysis have been investigated.

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Author information

Authors and Affiliations

  1. Département de Mathématiques, Institut Galilée, av. J.B. Clément, Université Paris Nord, Villetaneuse, F-93430, Germany

    Francesco Russo

  2. BIBOS, Universität Bielefeld, Bielefeld 1, D-33501, France

    Francesco Russo

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  1. Francesco Russo
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Editors and Affiliations

  1. TELECOM Portugal, Funchal(Madeira), Portugal

    Ana Isabel Cardoso

  2. CCM, Universidade da Madeira, Funchal(Madeira), Portugal

    Margarida de Faria

  3. Fakultät für Mathematik und Informatik, Universität Mannheim, Mannheim, Germany

    Jürgen Potthoff

  4. Centre de Physique Théorique, Ecole Polytechnique, Palaiseau, France

    Roland Sénéor

  5. CCM, Universidade da Madeira, Funchal(Madeira), Portugal

    Ludwig Streit

  6. BiBoS, Universität Bielefeld, Bielefeld, Germany

    Ludwig Streit

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© 1994 Springer Science+Business Media Dordrecht

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Russo, F. (1994). Colombeau Generalized Functions and Stochastic Analysis. In: Cardoso, A.I., de Faria, M., Potthoff, J., Sénéor, R., Streit, L. (eds) Stochastic Analysis and Applications in Physics. NATO ASI Series, vol 449. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0219-3_13

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  • DOI: https://doi.org/10.1007/978-94-011-0219-3_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4098-3

  • Online ISBN: 978-94-011-0219-3

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