# THE CONVENIENT SETTING FOR

@inproceedings{Kriegl2012THECS, title={THE CONVENIENT SETTING FOR}, author={Andreas Kriegl and Peter W. Michor and Armin Rainer}, year={2012} }

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 log-convex and of moderate growth: For C denoting either C (M) or C fMg , the category of C-mappings is cartesian closed in the sense thatC(E;C(F;G)) =C(E F;G) for convenient vector spaces. Applications to manifolds of mappings are given: The group ofC-dieomorphisms is a regular C-Lie group ifC C…

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## 10 Citations

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## References

SHOWING 1-10 OF 12 REFERENCES

Resolution of singularities in Denjoy-Carleman classes

- Mathematics
- 2001

Abstract
We show that a version of the desingularization theorem of Hironaka
$${\cal C}^\infty $$
holds for certain classes of
functions (essentially, for
subrings that exclude flat functions and…

Perturbation theory for normal operators

- Mathematics
- 2013

Let E 3 x 7! A(x) be a C -mapping with its values being un- bounded normal operators with common domain of denition and compact resolvent. Here C stands for C1, C! (real analytic), C(M)…

Über die Regularitatsbegriffe induktiver lokalkonvexer Sequenzen

- Mathematics
- 1978

This paper is concerned with some questions of regularity in increasing inductive sequences of locally convex spaces. It is shown that the various stronger terms of regularity coincide in case of…

The convenient setting for real analytic mappings

- Mathematics
- 1990

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…

The Logarithmic Integral

- Mathematics
- 1986

Preface Introduction 1. Jensen's formula 2. Szego's theorem 3. Entire functions of exponential type 4. Quasianalyticity 5. The moment problem on the real line 6. Weighted approximation on the real…

Composition in ultradifferentiable classes

- Mathematics
- 2014

We characterize stability under composition of ultradifferentiable classes defined by weight sequences $M$, by weight functions $\omega$, and, more generally, by weight matrices $\mathfrak{M}$, and…

A general approximation theorem of Whitney type

- Mathematics
- 2003

Dedicated to the memory of Klaus Floret Abstract. We show that Whitney's approximation theorem holds in a general setting including spaces of (ultra)differentiable functions and ultradistributions.…

Spaces of smooth functions of Denjoy-Carleman-type

- Philosophy, Physics
- 2009

Glatte Funktionen vom Denjoy-Carleman-Typ sind spezielle glatte Funktionen, die gemeinsam mit ihren Ableitungen ein gewisses Grosenwachstum erfullen. Dieses Wachstum wird durch eine Gewichtsfolge…