A convenient setting for real analytic mappings
泛函分析
2016-09-06 v1 经典分析与常微分方程
微分几何
摘要
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 smooth curves to smooth curves and real analytic curves to real analytic curves. Under mild completeness conditions the second requirement can be replaced by: real analytic along affine lines. Enclosed and necessary is a careful study of locally convex topologies on spaces of real analytic mappings. As an application we also present the theory of manifolds of real analytic mappings: the group of real analytic diffeomorphisms of a compact real analytic manifold is a real analytic Lie group.
引用
@article{arxiv.math/9201254,
title = {A convenient setting for real analytic mappings},
author = {Andreas Kriegl and Peter W. Michor},
journal= {arXiv preprint arXiv:math/9201254},
year = {2016}
}