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Introduction to “new generalized functions” and multiplication of distributions. (English) Zbl 0761.46021
Functional analysis and its applications, Lect. Int. Sch., Nice/Fr. 1986, 338-380 (1988).
[For the entire collection see Zbl 0731.00014.]
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 \({\mathcal G}(\Omega)={\mathcal E}_ M(\Omega)/{\mathcal N}_ M(\Omega)\), \({\mathcal E}_ M(\Omega)\) being the space of families of \(C^ \infty(\Omega)\)-functions with a parameter \(\varepsilon\in]0,1]\) with derivatives locally of order \(\leq\varepsilon^{-N}\), \(N\in\mathbb{N}\), and \({\mathcal N}(\Omega)\) being its suitable subspace.

46F05 Topological linear spaces of test functions, distributions and ultradistributions
46F99 Distributions, generalized functions, distribution spaces