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The Convenient Setting of Global Analysis
Introduction Calculus of smooth mappings Calculus of holomorphic and real analytic mappings Partitions of unity Smoothly realcompact spaces Extensions and liftings of mappings Infinite dimensional
Linear Spaces And Differentiation Theory
Preface Foundational Material Convenient Vector Spaces Multilinear Maps and Categorical Properties Calculus in Convenient Vector Spaces Differentiable Maps and Categorical Properties The Mackey
Choosing roots of polynomials smoothly
We clarify the question whether for a smooth curve of polynomials one can choose the roots smoothly and related questions. Applications to perturbation theory of operators are given.
The convenient setting for real analytic mappings
We present here "the" cartesian closed theory for real analytic mappings. It is based on the concept of real analytic curves in locally convex vector spaces. A mapping is real analytic, if it maps
We prove in a uniform way that all Denjoy{Carleman dieren- tiable function classes of Beurling type C (M) and of Roumieu type C fMg , admit a convenient setting if the weight sequence M = (Mk) is
The Riemannian geometry of orbit spaces. The metric, geodesics, and integrable systems
We investigate the rudiments of Riemannian geometry on orbit spaces $M/G$ for isometric proper actions of Lie groups on Riemannian manifolds. Minimal geodesic arcs are length minimising curves in the
Reflection groups on Riemannian manifolds
We investigate discrete groups G of isometries of a complete connected Riemannian manifold M which are generated by reflections, in particular those generated by disecting reflections. We show that
Smooth, real analytic and holomorphic mappings defined on non-open subsets of infinite dimensional vector spaces are treated.
The convenient setting for Denjoy–Carleman differentiable mappings of Beurling and Roumieu type
We prove in a uniform way that all Denjoy–Carleman differentiable function classes of Beurling type $$C^{(M)}$$C(M) and of Roumieu type $$C^{\{M\}}$$C{M}, admit a convenient setting if the weight
Smooth *-algebras
Looking for the universal covering of the smooth non-commutative torus leads to a curve of associative multiplications on the space O M (R) ∼= OC(R ) of Laurent Schwartz which is smooth in the