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

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.