$C$-distribution semigroups and $C$-ultradistribution semigroups in locally convex spaces

TL;DR

This paper explores the theory of $C$-distribution and $C$-ultradistribution semigroups within sequentially complete locally convex spaces, providing new theoretical insights and illustrative examples.

Contribution

It introduces new theoretical results on $C$-distribution and $C$-ultradistribution semigroups in locally convex spaces, expanding the mathematical framework.

Findings

Development of new theoretical properties

Examples illustrating the concepts

Extension of semigroup theory in locally convex spaces

Abstract

The main purpose of this paper is to investigate $C$-distribution semigroups and $C$-ultradistribution semigroups in the setting of sequentially complete locally convex spaces. There are a few important theoretical novelties in this field and there are given some interesting examples.