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arXiv · 1411.0854

On cosine families close to scalar cosine families

Wojciech Chojnacki
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Abstract

We prove that if two normed-algebra-valued cosine families indexed by a single Abelian group, of which one is bounded and comprised solely of scalar elements of the underlying algebra, differ in norm by less than $1$ uniformly in the parametrising index, then these families coincide.

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Wojciech Chojnacki. 2015-09-17. On cosine families close to scalar cosine families. https://doi.org/10.1017/s1446788715000038

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