Degenerate C-distribution cosine functions and degenerate C-ultradistribution cosine functions in 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. E(a, b) := λ ∈ C : ℜλ ≥ b, |ℑλ| ≤ e aℜλ (a, b > 0).