Dokument-ID Dokumenttyp Verfasser/Autoren Herausgeber Haupttitel Abstract Auflage Verlagsort Verlag Erscheinungsjahr Seitenzahl Schriftenreihe Titel Schriftenreihe Bandzahl ISBN Quelle der Hochschulschrift Konferenzname Quelle:Titel Quelle:Jahrgang Quelle:Heftnummer Quelle:Erste Seite Quelle:Letzte Seite URN DOI Abteilungen OPUS4-2863 Konferenzveröffentlichung Constales, Denis; Kraußhar, Rolf Sören Gürlebeck, Klaus; Könke, Carsten ON THE KLEIN-GORDON EQUATION ON THE 3-TORUS 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. 10 urn:nbn:de:gbv:wim2-20170314-28639 10.25643/bauhaus-universitaet.2863 In Zusammenarbeit mit der Bauhaus-Universität Weimar OPUS4-2846 Konferenzveröffentlichung Grob, Dennis; Constales, Denis; Kraußhar, Rolf Sören Gürlebeck, Klaus; Könke, Carsten THE HYPERCOMPLEX SZEGÖ KERNEL METHOD FOR 3D MAPPING PROBLEMS In this paper we present rudiments of a higher dimensional analogue of the Szegö kernel method to compute 3D mappings from elementary domains onto the unit sphere. This is a formal construction which provides us with a good substitution of the classical conformal Riemann mapping. We give explicit numerical examples and discuss a comparison of the results with those obtained alternatively by the Bergman kernel method. 7 urn:nbn:de:gbv:wim2-20170314-28464 10.25643/bauhaus-universitaet.2846 In Zusammenarbeit mit der Bauhaus-Universität Weimar OPUS4-2834 Konferenzveröffentlichung Cacao, Isabel; Constales, Denis; Kraußhar, Rolf Sören Gürlebeck, Klaus; Könke, Carsten A UNIFIED APPROACH FOR THE TREATMENT OF SOME HIGHER DIMENSIONAL DIRAC TYPE EQUATIONS ON SPHERES Using Clifford analysis methods, we provide a unified approach to obtain explicit solutions of some partial differential equations combining the n-dimensional Dirac and Euler operators, including generalizations of the classical time-harmonic Maxwell equations. The obtained regular solutions show strong connections between hypergeometric functions and homogeneous polynomials in the kernel of the Dirac operator. 8 urn:nbn:de:gbv:wim2-20170314-28343 10.25643/bauhaus-universitaet.2834 In Zusammenarbeit mit der Bauhaus-Universität Weimar