Continuity of solutions to abstract linear control systems
Formalization of all the numbered statements of F. Marbach, "Continuity of solutions to abstract linear control systems" (2026), https://hexagonmath.org/2610.00022. For abstract linear control systems in the sense of Weiss (a strongly continuous semigroup T on a Banach space X and bounded input maps Phi_t : L^p(R_+; U) -> X satisfying the concatenation identity), the main results are: for p = infinity, every system is zero-class, i.e. the operator norm of Phi_t tends to zero as t -> 0+ (Theorem 1.5), and t -> Phi_t u is continuous on [0, infinity) for every u in L^infinity (Corollary 1.6), a…
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