Extension of local smooth maps of Banach spaces

Genrich Belitskii; Victoria Rayskin

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arXiv · 1703.06299

Extension of local smooth maps of Banach spaces

Genrich Belitskii·Victoria Rayskin

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Abstract

It is known that smooth bump functions are absent in the majority of infinite-dimensional Banach spaces. This is an obstacle in the development of local analysis, in particular in the questions of extending local maps onto the whole space. We suggest an approach that substitutes bump functions with special maps, which we call K-maps. It allows us to extend smooth local maps from non-smooth spaces, such as $C^q[0,1], q=0,1,...$. We also prove the Borel lemma for spaces possessing K-maps.

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BibTeX RIS

Genrich Belitskii, Victoria Rayskin. 2017-03-18. Extension of local smooth maps of Banach spaces. https://arxiv.org/abs/1703.06299

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