Journal of Lie Theory

no. 1
A Category of Banach Space Functors
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 
@article{JOLT_2024_34_1_a9,
     author = {M. Garay and D. v. 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/}
}
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M. Garay; D. v. Straten. A Category of Banach Space Functors. Journal of Lie Theory, Volume 34 (2024) no. 1, pp. 207-236. doi: 10.5802/jolt.1333

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