• Corpus ID: 124921861

# THE CONVENIENT SETTING FOR

@inproceedings{Kriegl2012THECS,
title={THE CONVENIENT SETTING FOR},
author={Andreas Kriegl and Peter W. Michor and Armin Rainer},
year={2012}
}
• Published 2012
• Mathematics
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…
On algebras and groups of formal series over a groupo\"id and application to some spaces of cobordism
We develop here a concept of deformed algebras and their related groups through two examples. Deformed algebras are obtained from a fixed algebra by deformation along a family of indexes, through
The group of diffeomorphisms of a non-compact manifold is not regular
Abstract We show that a group of diffeomorphisms D on the open unit interval I, equipped with the topology of uniform convergence on any compact set of the derivatives at any order, is non-regular:
DEFORMED ALGEBRAS: EXAMPLES AND APPLICATION TO LAX EQUATIONS
We develop here a concept of deformed algebras through three examples and an application. Deformed algebras are obtained from a fixed algebra by deformation along a family of indexes, through formal
Remarks on the geometry and the topology of the loop spaces $H^{s}(S^1, N),$ for $s\leq 1/2.$
We first show that, for a fixed locally compact manifold $N,$ the space $L^2(S^1,N)$ has not the homotopy type odf the classical loop space $C^\infty(S^1,N),$ by two theorems: - the inclusion
Dif f + ( S 1 ) – PSEUDO-DIFFERENTIAL OPERATORS AND THE KADOMTSEV-PETVIASHVILI HIERARCHY
• Mathematics
• 2019
We establish a non-formal link between the structure of the group of Fourier integral operators Cl0,∗ odd(S 1, V )oDiff+(S) and the solutions of the Kadomtsev-Petviashvili hierarchy, using
Higher symmetries of symplectic Dirac operator
• Mathematics
• 2018
We construct in projective differential geometry of the real dimension 2 higher symmetry algebra of the symplectic Dirac operator acting on symplectic spinors. The higher symmetry differential
A Geometric Framework for the Inconsistency in Pairwise Comparisons
• Mathematics
ArXiv
• 2016
In this study, a pairwise comparison matrix is generalized to the case when coefficients create Lie group $G$, non necessarily abelian and basic criteria for finding a nearest consistent pairwise comparisons matrix are proposed.
On Mathematical structures on pairwise comparisons matrices with coefficients in a group arising from quantum gravity
We describe the mathematical properties of pairwise comparisons matrices with coefficients in an arbitrary group. We provide a vocabulary adapted for the description of main algebraic properties of
Differentiation on spaces of triangulations and optimized triangulations.
We describe a smooth structure, called Frolicher space, on CW complexes and spaces of triangulations. This structure enables differential methods for e.g. minimization of functionnals. As an
From infinitesimal symmetries to deformed symmetries of Lax-type equations
Using the procedure initiated in [14], we deform Lax-type equations though a scaling of the time parameter. This gives an equivalent (deformed) equation which is integrable in terms of power series

## 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
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
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
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
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