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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.

##### MSC:
 46F05 Topological linear spaces of test functions, distributions and ultradistributions 46F99 Distributions, generalized functions, distribution spaces
##### Keywords:
new generalized functions; quotient space