Extension of differentiable local mappings on linear topological spaces

2018/12/23 by Genrich Belitskii, Belitskii, Genrich, Victoria Rayskin +1
Mathematics · #26E15 #46B07 #58Bxx #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1812.11064

openalex publication_date 2018/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citeBR 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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