Differentiable mappings on products with different degrees of differentiability in the two factors

Abstract

We develop differential calculus of $C^{r,s}$-mappings on products of locally convex spaces and prove exponential laws for such mappings. As an application, we consider differential equations in Banach spaces depending on a parameter in a locally convex space. Under suitable assumptions, the associated flows are mappings of class $C^{r,s}$.

42 Pages, Latex, v2: Corrected several misprints and typos. The results remain unchanged

References in corpus (5)

• Lie groups over non-discrete topological fields
• Lie group structures on groups of smooth and holomorphic maps on non-compact manifolds
• The diffeomorphism group of a non-compact orbifold
• Implicit functions from topological vector spaces to Fréchet spaces in the presence of metric estimates
• Continuity of LF-algebra representations associated to representations of Lie groups

Cited by in corpus (26)

• The Lie group of bisections of a Lie groupoid
• Manifolds of mappings for continuum mechanics
• Regularity properties of infinite-dimensional Lie groups, and semiregularity
• The diffeomorphism group of a non-compact orbifold
• Lie groupoids of mappings taking values in a Lie groupoid
• Lie Theory for Asymptotic Symmetries in General Relativity: The BMS Group
• Extending Whitney's extension theorem: nonlinear function spaces
• Continuity of LF-algebra representations associated to representations of Lie groups
• Smooth approximations and their applications to homotopy types
• The Lie group of real analytic diffeomorphisms is not real analytic
• The Lie group structure of the Butcher group
• The geometry of characters of Hopf algebras
• Local Flexibility for Open Partial Differential Relations
• Overview of (pro-)Lie group structures on Hopf algebra character groups
• Lie Theory for Asymptotic Symmetries in General Relativity: The NU Group
• A ${\mathcal{C}}^k$-Seeley-Extension-Theorem for Bastiani's Differential Calculus
• Manifolds of absolutely continuous curves and the square root velocity framework
• Exponential laws for ultrametric partially differentiable functions and applications
• Convergence of Lie group integrators
• Linking Lie groupoid representations and representations of infinite-dimensional Lie groups
• Manifolds of mappings on cartesian products
• The Lie group of vertical bisections of a regular Lie groupoid
• A Lie group structure on the group of real analytic diffeomorphisms of a compact real analytic manifold with corners
• Exponential laws for spaces of differentiable functions on topological groups
• Smoothing operators for vector-valued functions and extension operators
• Lie groups of real analytic diffeomorphisms are $L^1$-regular