Non-standard version of Egorov algebra of generalized functions (Q6547681)

The author constructs a new non-standard version of Egorov's theory of algebras of generalized functions (originally introduced in [\textit{Yu. V. Egorov}, Russ. Math. Surv. 45, No. 5, 1--49 (1990; Zbl 0754.46034); translation from Usp. Mat. Nauk 45, No. 5(275), 3--40 (1990)]). Although the algebra itself coincides with the one introduced by \textit{H. Vernaeve} in [Proc. Edinb. Math. Soc., II. Ser. 46, No. 2, 373--378 (2003; Zbl 1058.46022)], the embedding of the space of distributions in the present paper is different. While Vernaeve's construction requires the underlying domain to be convex and open, the convexity assumption can be dropped here. On the other hand, the embedding in the present setting is not of Colombeau-type: only the pointwise product on the ring of polynomials (instead of on the space of all smooth functions) is preserved. The author also defines an analogue of Oberguggenberger's regular subalgebra \(\mathcal{G}^\infty\) in this setting.\N\NFor the entire collection see [Zbl 1537.35003].