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The aim of this book is to lay foundations of differential calculus in infinite dimensions and to discuss those applications in infinite dimensional differential geometry and global analysis which do… (More)
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. Table of contents
Smooth, real analytic and holomorphic mappings defined on non-open subsets of infinite dimensional vector spaces are treated.
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… (More)
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… (More)
The convenient setting for smooth mappings, holomorphic mappings, and real analytic mappings in infinite dimension is sketched. Infinite dimensional manifolds are discussed with special emphasis on… (More)
We show that the roots of any smooth curve of polynomials with real roots only can be parametrized twice differentiable (but not better). In  we claimed that there exists a smooth curve of… (More)
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… (More)
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… (More)
The theory of product preserving functors and Weil functors is partly extended to infinite dimensional manifolds, using the theory of C∞-algebras.