@Article{dbt_mods_00037103,
  author = 	{Constales, Denis
		and Krau{\ss}har, Rolf S{\"o}ren
		and {Internationales Kolloquium {\"u}ber Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 07. bis 09.07. 2009, Bauhaus-Universit{\"a}t Weimar}},
  editor = 	{G{\"u}rlebeck, Klaus
		and K{\"o}nke, Carsten
		and G{\"u}rlebeck, Klaus
		and Koenke, Carsten},
  title = 	{On the Klein-Gordon equation on the 3-torus},
  journal = 	{Internationales Kolloquium {\"u}ber Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 07. bis 09.07.2009, Bauhaus-Universit{\"a}t Weimar},
  year = 	{2010},
  month = 	{Jul},
  day = 	{14},
  address = 	{Weimar},
  volume = 	{18, 2009},
  keywords = 	{Angewandte Informatik; Angewandte Mathematik; Architektur <Informatik>; Computerunterst{\"u}tztes Verfahren; Building Information Modeling},
  abstract = 	{In this paper we consider the time independent Klein-Gordon equation on some conformally flat 3-tori with given boundary data. We set up an explicit formula for the fundamental solution. We show that we can represent any solution to the homogeneous Klein-Gordon equation on the torus as finite sum over generalized 3-fold periodic elliptic functions that are in the kernel of the Klein-Gordon operator. Furthermore we prove Cauchy and Green type integral formulas and set up a Teodorescu and Cauchy transform for the toroidal Klein-Gordon operator. These in turn are used to set up explicit formulas for the solution to the inhomogeneous version of the Klein-Gordon equation on the 3-torus.},
  issn = 	{1611-4086},
  doi = 	{10.25643/bauhaus-universitaet.2863},
  url = 	{https://www.db-thueringen.de/receive/dbt_mods_00037103},
  url = 	{https://doi.org/10.25643/bauhaus-universitaet.2863},
  file = 	{:https://www.db-thueringen.de/servlets/MCRFileNodeServlet/dbt_derivate_00043253/8-final-man_106_pdfa.pdf:PDF},
  language = 	{en}
}