Degenerate $C$-ultradistribution semigroups in locally convex spaces

TL;DR

This paper studies degenerate $C$-ultradistribution semigroups in locally convex spaces, focusing on cases where the regularizing operator is not injective and the generator is multivalued, including exponential variants.

Contribution

It introduces the theory of degenerate $C$-ultradistribution semigroups with non-injective regularizing operators and multivalued generators in locally convex spaces.

Findings

Extended the class of $C$-ultradistribution semigroups to degenerate cases.

Analyzed properties of semigroups with non-injective regularizing operators.

Explored exponential degenerate $C$-ultradistribution semigroups.

Abstract

The main subject in this paper are degenerate $C$-ultradistribution semigroups in barreled sequentially complete locally convex spaces. Here, the regularizing operator $C$ is not necessarily injective and the infinitesimal generator is multivalued linear operator. We also consider exponential degenerate $C$-ultradistribution semigroups.