arXiv subjects

Matthieu F. Pinaud

Publications and source records attributed to Matthieu F. Pinaud.

5 recordsLinked to original sources

arXiv2026

On $L^p$-spaces of functions with values in locally convex spaces

We study Lusin-measurable functions with values in locally convex spaces. In particular, the behavior of pointwise limits of sequences of Lusin-measurable functions and exhibit pathological phenomena arising in the nonmetrizable setting. Moreover, we establish approximation and density results for $L^p$-spaces constructed with this notion of measurability, including the density of simple functions in Hausdorff locally convex spaces and convergence results obtained through dyadic approximations.

math.FA↗

arXiv2026

Controllability of time-varying lumped semilinear systems

In this work we are concerned with the controllability of time-varying lumped control systems governed by a semilinear differential equation. We consider the semilinear system as a perturbation of a linear system. Assuming the underlying linear system is controllable, and the nonlinear forcing function satisfies a boundedness condition which is adapted to the underlying linear system, we show that the semilinear system is also approximately controllable

math.OC↗

arXiv2026

Evolution families and variation of constants formula for abstract functional differential equations with time-dependent infinite delay

In this paper, we consider a class of first-order abstract retarded functional differential equations in Banach spaces, incorporating a time-dependent infinite delay governed by a regulated function. We establish the existence of mild solutions for the nonlinear equation and show that the family of solution maps for the linear equation forms a well-defined evolution family of bounded linear operators on an appropriate phase space. Furthermore, we leverage this evolution family to prove a variation of constants formula for the inhomogeneous linear problem.

math.CA↗

arXiv2026

Manifolds of absolutely continuous functions with values in an infinite-dimensional manifold and regularity properties of half-Lie groups

For $p\in [1,\infty]$, we define a smooth manifold structure on the set $AC_{L^p}([a,b],N)$ of absolutely continuous functions $γ\colon [a,b]\to N$ with $L^p$-derivatives for all real numbers $a<b$ and each smooth manifold $N$ modeled on a sequentially complete locally convex topological vector space, such that $N$ admits a local addition. Smoothness of natural mappings between spaces of absolutely continuous functions is discussed, like superposition operators $AC_{L^p}([a,b],N_1)\to AC_{L^p}([a,b],N_2)$, $η\mapsto f\circ η$, for a smooth map $f\colon N_1\to N_2$. For $1\leq p <\infty$ and $r\in \mathbb{N}$ we show that the right half-Lie groups $\text{Diff}_K^r(\mathbb{R})$ and $\text{Diff}^r(M)$ are $L^p$-semiregular. Here $K$ is a compact subset of $\mathbb{R}$ and $M$ is a compact smooth manifold. An $L^p$-semiregular half-Lie group $G$ admits an evolution map $\text{Evol}:L^p([0,1],T_e G)\to AC_{L^p}([0,1],G)$, where $e$ is the neutral element of $G$. For the preceding examples, the evolution map $\text{Evol}$ is continuous.

math.FA↗

arXiv2025

Manifolds of mappings associated with real-valued function spaces and natural mappings between them

Let $M$ be a compact smooth manifold with corners and $N$ be a finite dimensional smooth manifold without boundary which admits local addition. We define a smooth manifold structure to general sets of continuous mapings $\mathcal{F}(M,N)$ whenever functions spaces $\mathcal{F}(U,\mathbb{R})$ on open subsets $U\subseteq [0,\infty)^n$ are given, subject to simple axioms. Construction and properties of spaces of sections and smoothness of natural mappings between spaces $\mathcal{F}(M,N)$ are discussed, like superposition operators $\mathcal{F}(M,f):\mathcal{F}(M,N_1)\to \mathcal{F}(M,N_2)$, $η\mapsto f\circ η$ for smooth maps $f:N_1\to N_2$.

math.DG↗