Fixed points of the 𝑝-adic 𝑞-bracket

Brussel, Eric

doi:10.1090/S0002-9939-2011-11012-8

Fixed points of the ${p}$-adic ${q}$-bracket
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by Eric Brussel PDF

Proc. Amer. Math. Soc. 140 (2012), 1501-1511 Request permission

Abstract:

The $q$-bracket $[X]_q\!:\!\textrm {O}_{\mathbb {C}_p}\!\to \!\textrm {O}_{\mathbb {C}_p}$, which is the $q$-analog of the identity function, is also a norm-preserving isometry, for each $q\in \textrm {B}(1,p^{-1/(p-1)})$. In this paper we investigate its fixed points.

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