Let be a discretely valued nonarchimedean field. We give an explicit description of analytic functions whose norm is bounded by a given real number on tubes of reduced -analytic spaces associated to special formal schemes (including -affinoid spaces as well as open polydiscs). As an application we study the connectedness of these tubes. In the discretely valued case, this generalizes a result of Siegfried Bosch. We use as a main tool a result of Aise Johan de Jong relating formal and analytic functions on special formal schemes and a generalization of de Jong’s result which is proved in the joint appendix with Christian Kappen.
"Analytic functions on tubes of nonarchimedean analytic spaces." Algebra Number Theory 11 (3) 657 - 683, 2017. https://doi.org/10.2140/ant.2017.11.657