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Extension of differentiable local mappings on linear topological spaces

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arxiv 1812.11064 v1 pith:KDOECXHC submitted 2018-12-23 math.FA

Genrich Belitskii , Victoria Rayskin This is my paper · ORCID
classification math.FA
keywords spacesbumpextensionfunctionslinearlocalmapstopological
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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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  1. New Method of Smooth Extension of Local Maps on Linear Topological Spaces. Applications and Examples

    math.DS 2019-08 conditional novelty 4.0 of 10

    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.

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