A new theory of generalized functions
Let \(\Omega\) be the domain in \({\mathbb{R}}^ n\). In this paper the new space of generalized functions \({\mathcal G}(\Omega)\) is defined as follows: Consider the space of infinite differentiable functions defined on (0,1)\(\times \Omega\). Two functions are called equivalent, if they coincide on the set (0,\(\epsilon\))\(\times \Omega\) for some positive \(\epsilon\). The generalized function space \({\mathcal G}(\Omega)\) is the quotient space of the above space with respect to this equivalence relation. The space of Schwartz distributions \({\mathcal D}'(\Omega)\) is imbedded in the space \({\mathcal G}(\Omega)\) and an operation of multiplication for elements of \({\mathcal G}(\Omega)\) is determined [see also \textit{M. S. Burgin}, Dokl. Akad. Ukrain. SSR, Ser. A 1987, No.7, 5-9 (1987; Zbl 0628.46037)]. The author states that the new theory of distributions describe more adequately physical reality and gives opportunity to define the generalized solution for some equations, what is impossible in classical theory.
scientific article; zbMATH DE number 4177883