Quasi-equicontinous exponential families of generalized function $C$-semigroups in locally convex spaces

TL;DR

This paper investigates (q-)exponential $C$-distribution and ultradistribution semigroups in locally convex spaces, providing new examples and applications to extend existing theoretical frameworks.

Contribution

It introduces new classes of (q-)exponential $C$-semigroups in locally convex spaces, expanding the theoretical understanding and practical examples of these operator families.

Findings

Established properties of (q-)exponential $C$-distribution semigroups

Provided numerous examples and applications

Extended previous theoretical results

Abstract

Our main goal in this paper is to investigate the (q-)exponential $C$-distribution semigroups and (q-)exponential $C$-ultradistribution semigroups in the setting of sequentially complete locally convex spaces. We contribute to previous work and the work of many other authors, providing additionally plenty of various examples and applications of obtained results.