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

2025/06/03 by Matthieu F. Pinaud, Pinaud, Matthieu F.
Mathematics · #Advanced Banach Space Theory #Fixed Point Theorems Analysis

paper · pdf · doi:10.48550/arxiv.2506.03366

Abstract

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 F(M,N) whenever functions spaces F(U,ℝ) on open subsets U⊆ [0,∞)ⁿ are given, subject to simple axioms. Construction and properties of spaces of sections and smoothness of natural mappings between spaces F(M,N) are discussed, like superposition operators F(M,f):F(M,N₁)→ F(M,N₂), η↦ f∘ η for smooth maps f:N₁→ N₂.

Citations

• Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups
• Lie groups of real analytic diffeomorphisms are L¹-regular
• Smoothing operators for vector-valued functions and extension operators

Related

• Algebraic Smooth Structures 1
• Yet More Smooth Mapping Spaces and Their Smoothly Local Properties
• Smoothing operators for vector-valued functions and extension operators
• Formal manifolds: local structure of morphisms, and formal submanifolds
• Reeb spaces of smooth functions on manifolds II