Extension of smooth functions in infinite dimensions II: manifolds

Volume 150 / 2002

C. J. Atkin Studia Mathematica 150 (2002), 215-241 MSC: Primary 46T20. DOI: 10.4064/sm150-3-2

Abstract

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

Authors

  • C. J. AtkinSchool of Mathematical and Computing Sciences
    Victoria University of Wellington
    P.O. Box 600, Wellington, New Zealand
    e-mail

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