Proves a weighted Nachbin theorem establishing universal approximation of differentiable maps from weighted infinite-dimensional manifolds to Banach spaces, including derivatives, with applications to non-anticipative path functionals and signature methods.
Fundamentals of submersions and immersions between infinite-dimensional manifolds
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abstract
We define submersions f between manifolds M and N modelled on locally convex spaces. If the range N is finite-dimensional or a Banach manifold, then these coincide with the naive notion of a submersion. We study pre-images of submanifolds under submersions and pre-images under mappings whose differentials have dense image. An infinite-dimensional version of the constant rank theorem is provided. We also construct manifold structures on homogeneous spaces G/H of infinite-dimensional Lie groups. Some fundamentals of immersions between infinite-dimensional manifolds are developed as well.
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2026 1verdicts
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Weighted universal approximation of differentiable maps on infinite-dimensional manifolds
Proves a weighted Nachbin theorem establishing universal approximation of differentiable maps from weighted infinite-dimensional manifolds to Banach spaces, including derivatives, with applications to non-anticipative path functionals and signature methods.