Geodesic
A $\mathcal {C}^k$-seeley-extension-theorem for Bastiani’s differential calculus
Canadian journal of mathematics, Tome 75 (2023) no. 1, pp. 170-201

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DOI

We generalize a classical extension result by Seeley in the context of Bastiani’s differential calculus to infinite dimensions. The construction follows Seeley’s original approach, but is significantly more involved as not only $C^k$-maps (for ) on (subsets of) half spaces are extended, but also continuous extensions of their differentials to some given piece of boundary of the domains under consideration. A further feature of the generalization is that we construct families of extension operators (instead of only one single extension operator) that fulfill certain compatibility (and continuity) conditions. Various applications are discussed as well.
DOI : 10.4153/S0008414X21000596
Mots-clés : Extension of functions in infinite-dimensional spaces, Seeley’s extension theorem, Bastiani’s differential calculus 
Hanusch, Maximilian. A $\mathcal {C}^k$-seeley-extension-theorem for Bastiani’s differential calculus. Canadian journal of mathematics, Tome 75 (2023) no. 1, pp. 170-201. doi: 10.4153/S0008414X21000596
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     year = {2023},
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