On diffeologies from infinite dimensional geometry to PDE constrained optimization
We review how diffeologies complete the settings classically used from infinite dimensional
geometry to partial differential equations, based on classical settings of functional analysis …
geometry to partial differential equations, based on classical settings of functional analysis …
On the geometry of pseudodifferential operators based on renormalized traces
JP Magnot - arXiv preprint arXiv:2007.00387, 2020 - arxiv.org
In this article, we examine the geometry of a group of Fourier-integral operators, which is the
central extension of $ Diff (S^ 1) $ with a group of classical pseudo-differential operators of …
central extension of $ Diff (S^ 1) $ with a group of classical pseudo-differential operators of …
On smooth infinite dimensional grassmannians, splittings and non-commutative generalized cross-ratio mappings
JP Magnot - arXiv preprint arXiv:2404.16888, 2024 - arxiv.org
We describe basic diffeological structures related to splittings and Grassmannians for infinite
dimensional vector spaces. We analyze and expand the notion of non-commutative cross …
dimensional vector spaces. We analyze and expand the notion of non-commutative cross …
On the geometry of diffeological vector pseudo-bundles and infinite dimensional vector bundles: automorphisms, connections and covariant derivatives
JP Magnot - arXiv preprint arXiv:2207.06824, 2022 - arxiv.org
We consider here the category of diffeological vector pseudo-bundles, and study a possible
extension of classical differential geometric tools on finite dimensional vector bundles …
extension of classical differential geometric tools on finite dimensional vector bundles …
On diffeological principal bundles of non-formal pseudo-differential operators over formal ones
JP Magnot - arXiv preprint arXiv:2207.07015, 2022 - arxiv.org
We describe the structure of diffeological bundle of non formal classical pseudo-differential
operators over formal ones, and its structure group. For this, we give few results on …
operators over formal ones, and its structure group. For this, we give few results on …
On the Cauchy problem for a Kadomtsev-Petviashvili hierarchy on non-formal operators and its relation with a group of diffeomorphisms
JP Magnot, EG Reyes - arXiv preprint arXiv:1808.03791, 2018 - arxiv.org
We establish a rigorous link between infinite-dimensional regular Fr\" olicher Lie groups built
out of non-formal pseudodifferential operators and the Kadomtsev-Petviashvili hierarchy. We …
out of non-formal pseudodifferential operators and the Kadomtsev-Petviashvili hierarchy. We …
[PDF][PDF] a review of On diffeological principal bundles of non-formal pseudo-differential operators over formal ones by Magnot, Jean-Pierre
西村泰一， ニシムラヒロカズ - zbMATH Open, 2023 - tsukuba.repo.nii.ac.jp
53C05 Connections (general theory) 57R55 Differentiable structures in differential topology
58B05 Homotopy and topological questions for infinite-dimensional manifolds 58B10 …
58B05 Homotopy and topological questions for infinite-dimensional manifolds 58B10 …