2020/07/30 by Helge Glöckner, Glockner, Helge · 1 citation
Mathematics · #22E65 (primary) #28B05 #34A12 #34H05 #46E20 #46E40 (secondary) #Advanced Banach Space Theory #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results
paper · pdf · doi:10.48550/arxiv.2007.15611
openalex publication_date 2020/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a compact, real analytic manifold and G be the Lie group of all real-analytic diffeomorphisms of M, which is modelled on the space \mathfrak g of real-analytic vector fields on M. We study flows of time-dependent real-analytic vector fields on M which are integrable functions in time, and their dependence on the time-dependent vector field. Notably, we show that the Lie group G is L1-regular in the sense that each [γ] in L1([0,1],\mathfrak g) has an evolution which is an absolutely continuous G-valued function on [0,1] and depends smoothly on [γ]. As tools for the proof, we develop new results concerning L1-regularity of infinite-dimensional Lie groups, and new results concerning the continuity and complex analyticity of non-linear mappings on locally convex direct limits.