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Zbl 0761.46021
Colombeau, J.F.
Introduction to ``new generalized functions'' and multiplication of distributions. (English)
[A] Functional analysis and its applications, Lect. Int. Sch., Nice/Fr. 1986, 338-380 (1988).

[For the entire collection see Zbl 0731.00014.]\par This is a lecture concerning various aspects of application of the ``new generalized functions'' (n.g.f.), introduced by the author 1985. The space of all n.g.s. is defined as the quotient space ${\cal G}(\Omega)={\cal E}\sb M(\Omega)/{\cal N}\sb M(\Omega)$, ${\cal E}\sb M(\Omega)$ being the space of families of $C\sp \infty(\Omega)$-functions with a parameter $\varepsilon\in]0,1]$ with derivatives locally of order $\leq\varepsilon\sp{-N}$, $N\in\bbfN$, and ${\cal N}(\Omega)$ being its suitable subspace.
[J.Musielak (Poznań)]

MSC 2000:: *46F05 Topological linear spaces of test functions and distributions
46F99 Generalized functions, etc.

Keywords: new generalized functions; quotient space

Citations: Zbl 0731.00014

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