Degenerate $C$-distribution cosine functions and degenerate $C$-ultradistribution cosine functions in locally convex spaces

TL;DR

This paper studies degenerate $C$-distribution cosine functions and their ultradistribution counterparts in locally convex spaces, focusing on their generators and regularizing operators, including exponential subclasses.

Contribution

It introduces a new framework for degenerate $C$-(ultra)distribution cosine functions with multivalued generators and non-injective regularizing operators in locally convex spaces.

Findings

Characterization of generators as multivalued linear operators

Extension to exponential subclasses of functions

Analysis in barreled sequentially complete locally convex spaces

Abstract

The main purpose of this paper is to investigate degenerate $C$-(ultra)distribution cosine functions in the setting of barreled sequentially complete locally convex spaces. In our approach, the infinitesimal generator of a degenerate $C$-(ultra)distribution cosine function is a multivalued linear operator and the regularizing operator $C$ is not necessarily injective. We provide a few important theoretical novelties, considering also exponential subclasses of degenerate $C$-(ultra)distribution cosine functions.