Gardiner, Stephen J.Stephen J.GardinerRender, HermannHermannRender2015-09-282018-01-152015 Elsev2016-01-15Journal of Mathematical Analysis and Applicationshttp://hdl.handle.net/10197/7132Suppose that a harmonic function h on a finite cylinder vanishes on the curved part of the boundary. This paper answers a question of Khavinson by showing that h then has a harmonic continuation to the infinite strip bounded by the hyperplanes containing the flat parts of the boundary. The existence of this extension is established by an analysis of the convergence properties of a double series expansion of the Green function of an infinite cylinder beyond the domain itself.enThis is the author’s version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Mathematical Analysis and Applications (VOL 433, ISSUE 2, (2015)) DOI: 10.1016/j.jmaa.2015.08.077.Harmonic continuationGreen functionCylindrical harmonicsJournal Article43321870188210.1016/j.jmaa.2015.08.0772015-09-22https://creativecommons.org/licenses/by-nc-nd/3.0/ie/