Journal of Lie Theory

no. 1
A Category of Banach Space Functors
Mauricio Garay1; Duco van Straten2
1Institut Fibonacci, Bures-sur-Yvette, France
2Institut für Mathematik, Johannes-Gutenberg-Universität, Mainz, Germany
Journal of Lie Theory, Volume 34 (2024) no. 1, pp. 207-236
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.
DOI: 10.5802/jolt.1333
Classification: 37J40
Keywords: Infinite dimensional Lie groups, dynamical systems, KAM theory, normal forms, versal deformations

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, Volume 34 (2024) no. 1, pp. 207-236. doi: 10.5802/jolt.1333
@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},
     doi = {10.5802/jolt.1333},
     zbl = {1540.18010},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1333/}
}
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  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1333/
DO  - 10.5802/jolt.1333
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 https://jolt.centre-mersenne.org/articles/10.5802/jolt.1333/
%R 10.5802/jolt.1333
%F JOLT_2024_34_1_a9

Cited by Sources: