Blid maps, a replacement for smooth bump functions, extend local smooth maps to global maps on spaces like C[0,1] and support a weakened bump-function condition in linearization theorems.
Extension of differentiable local mappings on linear topological spaces
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abstract
Usually, for extension of local maps, one uses multiplication by so called bump functions. However, majority of infinite-dimensional linear topological spaces do not have smooth bump functions. Therefore, in \cite{BR} we suggested a new approach for Banach spaces, based on the composition with locally identical maps. In the present work we discuss a possibility of generalization of this method for arbitrary spaces and applications of this theory.
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math.DS 1years
2019 1verdicts
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New Method of Smooth Extension of Local Maps on Linear Topological Spaces. Applications and Examples
Blid maps, a replacement for smooth bump functions, extend local smooth maps to global maps on spaces like C[0,1] and support a weakened bump-function condition in linearization theorems.