# The convenient setting for real analytic mappings

@article{Kriegl1990TheCS, title={The convenient setting for real analytic mappings}, author={Andreas Kriegl and Peter W. Michor}, journal={Acta Mathematica}, year={1990}, volume={165}, pages={105-159} }

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 ane lines. Enclosed and necessary is a careful study of locally convex topologies on spaces of real analytic mappings. As…

## 63 Citations

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## References

SHOWING 1-10 OF 70 REFERENCES

On the group of real analytic diffeomorphisms of a compact real analytic manifold

- Mathematics
- 1982

In this paper we exhibit a Lie group structure on the group of real analytic diffeomorphisms of a compact real analytic manifold. Further, we show that a variant of the Kupka-Smale theorem holds for…

The moment mapping for unitary representations

- Mathematics
- 1990

For any unitary representation of an arbitrary Lie group I construct a moment mapping from the space of smooth vectors of the representation into the dual of the Lie algebra. This moment mapping is…

Die richtigen Räume für Analysis im Unendlich-Dimensionalen

- Mathematics
- 1982

The aim of this paper is to characterize those locally convex spaces, which have the following properties. 1. Any curve, which is differentiable if composed with continuous linear forms, is…

Gauge Theory for Diffeomorphism Groups

- Mathematics
- 1988

We consider fibre bundles without structure group and develop the theory of connections, curvature, parallel transport, (nonlinear) frame bundle, the gauge group and it’s action on the space of…

Linear Spaces And Differentiation Theory

- Mathematics
- 1988

Preface Foundational Material Convenient Vector Spaces Multilinear Maps and Categorical Properties Calculus in Convenient Vector Spaces Differentiable Maps and Categorical Properties The Mackey…

The analysis of linear partial differential operators

- Physics
- 1990

the analysis of linear partial differential operators i distribution theory and fourier rep are a good way to achieve details about operating certainproducts. Many products that you buy can be…

Eine kartesisch abgeschlossene Kategorie glatter Abbildungen zwischen beliebigen lokalkonvexen Vektoräumen

- Mathematics
- 1983

This paper is a continuation of [6], in which I identified thec∞-complete bornological locally convex spaces (in short: 1cs) as the right ones for infinite dimensional analysis. Here I discuss smooth…

A convenient setting for holomorphy

- Mathematics
- 1985

© Andrée C. Ehresmann et les auteurs, 1985, tous droits réservés. L’accès aux archives de la revue « Cahiers de topologie et géométrie différentielle catégoriques » implique l’accord avec les…

Nonlinear Fourier analysis

- Mathematics
- 1989

On presente l'analyse de Fourier non lineaire sur un certain nombre d'exemples. On etudie les techniques generales. On considere certains aspects de la theorie de Littlewood-Paley

Sur certains espaces de fonctions holomorphes. I.

- 1953

1. Sujet et plan. Get article est destine a apporter quelques generalisations et complements a Γarticle de G. K the sur le meme sujet (c. f. [7])). II a ete congu neanmoins de fa£on independante, a…