2009
DOI: 10.1016/j.jfa.2009.03.003
|View full text |Cite
|
Sign up to set email alerts
|

The convenient setting for non-quasianalytic Denjoy–Carleman differentiable mappings

Abstract: For Denjoy-Carleman differentiable function classes C M where the weight sequence M = (M k ) is logarithmically convex, stable under derivations, and non-quasianalytic of moderate growth, we prove the following: A mapping is C M if it maps C M -curves to C M -curves. The category of C M -mappings is cartesian closed in the sense that C M (E, C M (F, G)) ∼ = C M (E × F, G) for convenient vector spaces. Applications to manifolds of mappings are given: The group of C M -diffeomorphisms is a C M -Lie group but not… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
2
1

Citation Types

1
76
0

Year Published

2011
2011
2020
2020

Publication Types

Select...
6
1

Relationship

3
4

Authors

Journals

citations
Cited by 41 publications
(77 citation statements)
references
References 15 publications
1
76
0
Order By: Relevance
“…The wish to prove the results of this paper was the main motivation for us to work on [16] and [17].…”
Section: Of Each A(t) and Such That A(t) * = A(t) In The Self-adjoinmentioning
confidence: 95%
See 2 more Smart Citations
“…The wish to prove the results of this paper was the main motivation for us to work on [16] and [17].…”
Section: Of Each A(t) and Such That A(t) * = A(t) In The Self-adjoinmentioning
confidence: 95%
“…Then C Q and C L are closed under composition and allow for the implicit function theorem. See [17] or [16] and references therein.…”
Section: Then the Eigenvalues Of A(t) Can Be Parameterized Twice Diffmentioning
confidence: 99%
See 1 more Smart Citation
“…For these classes we have developed a calculus in infinite dimensions beyond Banach spaces in [24,26,25] which is heavily based on composition: A smooth mapping f is of class E {M} if and only if f • p ∈ E {M} for all E {M} Banach plots (i.e., mappings defined in open subsets of Banach spaces); accordingly for E (M) . Sometimes curves suffice.…”
Section: Introductionmentioning
confidence: 99%
“…The exponential law (1) is well-known in the categories of C ∞ , real analytic, and holomorphic functions; see [8]. In [9][10][11] we established the exponential law (1) for local Denjoy-Carleman classes C [M] , provided that M = (M k ) is weakly log-convex and has moderate growth. (The notation C [M] stands for the classes C {M} of Roumieu type as well as for the classes C (M) of Beurling type, cf.…”
Section: Introductionmentioning
confidence: 99%