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Extension of smooth functions in infinite dimensions II: manifolds

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Atkin C.

Studia Mathematica

2002

tom 150

nr 3

215-241

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.

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

100%

Atkin C.

Studia Mathematica

2001

tom 146

nr 3

201-226

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.

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2 Studia Mathematica

2 Atkin C.

1 2002

1 2001

Wyniki wyszukiwania

Extension of smooth functions in infinite dimensions II: manifolds

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