We introduce a sheaf theoretic viewpoint on functional analysis designed for infinite dimensional Lie group actions. We develop functional calculus for Banach space valued functors and, in particular, prove the existence of an exponential map for a certain class of operators that generalise first order partial differential operators. These results can be used for proving normal forms and versal deformations theorems in KAM theory.
Classification :
37J40
Mots-clés :
Infinite dimensional Lie groups, dynamical systems, KAM theory, normal forms, versal deformations
Affiliations des auteurs :
Mauricio Garay
1
;
Duco van Straten
2
1
Institut Fibonacci, Bures-sur-Yvette, France
2
Institut für Mathematik, Johannes-Gutenberg-Universität, Mainz, Germany
Mauricio Garay; Duco van Straten. A Category of Banach Space Functors. Journal of Lie Theory, Tome 34 (2024) no. 1, pp. 207-236. http://geodesic.mathdoc.fr/item/JOLT_2024_34_1_a9/
@article{JOLT_2024_34_1_a9,
author = {Mauricio Garay and Duco van Straten},
title = {A {Category} of {Banach} {Space} {Functors}},
journal = {Journal of Lie Theory},
pages = {207--236},
year = {2024},
volume = {34},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2024_34_1_a9/}
}
TY - JOUR
AU - Mauricio Garay
AU - Duco van Straten
TI - A Category of Banach Space Functors
JO - Journal of Lie Theory
PY - 2024
SP - 207
EP - 236
VL - 34
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2024_34_1_a9/
ID - JOLT_2024_34_1_a9
ER -
%0 Journal Article
%A Mauricio Garay
%A Duco van Straten
%T A Category of Banach Space Functors
%J Journal of Lie Theory
%D 2024
%P 207-236
%V 34
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2024_34_1_a9/
%F JOLT_2024_34_1_a9
