{"id":"palomar/PALOMAR-2026-10-03-000001","url":"https://github.com/frederic-marbach/alcs/tree/bda56576f8b2730b73a55f273511c80fabbe56f4","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-03-000001-v2.json","repo":"https://github.com/frederic-marbach/alcs","tags":["math.OC","math.FA","msc:93C25","msc:47D06","msc:93C05","msc:46B45","control-theory","functional-analysis","semigroups","lean-formalization"],"score":0,"title":"Continuity of solutions to abstract linear control systems","trust":"high","domain":"math.OC","source":"palomar","authors":["Frédéric Marbach"],"reviews":0,"subject":"math.OC","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-03","reactions":{},"formalized":true,"formalizes":[{"title":"Continuity of solutions to abstract linear control systems","identifier":"https://hexagonmath.org/2610.00022","relationship":"formalizes"}]}