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Extension of smooth functions in infinite dimensions, I: unions of convex sets

C. J. Atkin — 2001

Studia Mathematica

Let f be a smooth function defined on a finite union U of open convex sets in a locally convex Lindelöf space E. If, for every x ∈ U, the restriction of f to a suitable neighbourhood of x admits a smooth extension to the whole of E, then the restriction of f to a union of convex sets that is strictly smaller than U also admits a smooth extension to the whole of E.

Extension of smooth functions in infinite dimensions II: manifolds

C. J. Atkin — 2002

Studia Mathematica

Let M be a separable C ∞ Finsler manifold of infinite dimension. Then it is proved, amongst other results, that under suitable conditions of local extensibility the germ of a C ∞ function, or of a C ∞ section of a vector bundle, on the union of a closed submanifold and a closed locally compact set in M, extends to a C ∞ function on the whole of M.

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