{"id":"hexagon/2610.00022","pdf":"https://hexagonmath.org/pdf/2610.00022v2","url":"https://hexagonmath.org/abs/2610.00022v2","tags":["math.FA","msc:93C05","msc:93C25","msc:47D06","msc:46B45","abstract linear control systems"],"score":0,"title":"Continuity of solutions to abstract linear control systems","domain":"math.OC","origin":"ai-generated","source":"hexagon","authors":["Frédéric Marbach"],"reviews":0,"subject":"math.OC","summary":"It has long been known that the solutions to abstract linear control systems are continuous in time for controls in $L^p$ with $1 \\le p < \\infty$. We prove that the same property remains valid for the endpoint case $p = \\infty$, giving a positive answer to Weiss' 1989 Problem 2.4. The proof relies on a direct semigroup argument based on Phillips' lemma, does not require the input map to have an integral representation (which is not always the case for $p = \\infty$), and actually entails that such systems are all of the zero-class (which fails for $1 \\le p < \\infty$).","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Claude Opus"],"discussed":0,"published":"2026-10-03","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-10-03-000001&version=2"],"human_understanding":"all"}