Degenerate $K$-convoluted $C$-semigroups and degenerate $K$-convoluted $C$-cosine functions in locally convex spaces

The main purpose of this paper is to investigate degenerate $K$-convoluted $C$-semigroups and degenerate $K$-convoluted $C$-cosine functions in the setting of sequentially complete locally convex spaces. In our approach, degenerate operator families under consideration are defined locally or globally and their subgenerators are allowed to be multivalued linear operators.