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 OPUS4-2838 Konferenzveröffentlichung De Schepper, Nele; Brackx, Fred; Sommen, Frank Gürlebeck, Klaus; Könke, Carsten THE FOURIER-BESSEL TRANSFORM In this paper we devise a new multi-dimensional integral transform within the Clifford analysis setting, the so-called Fourier-Bessel transform. It appears that in the two-dimensional case, it coincides with the Clifford-Fourier and cylindrical Fourier transforms introduced earlier. We show that this new integral transform satisfies operational formulae which are similar to those of the classical tensorial Fourier transform. Moreover the L2-basis elements consisting of generalized Clifford-Hermite functions appear to be eigenfunctions of the Fourier-Bessel transform. 18 urn:nbn:de:gbv:wim2-20170314-28387 10.25643/bauhaus-universitaet.2838 In Zusammenarbeit mit der Bauhaus-Universität Weimar OPUS4-2837 Konferenzveröffentlichung De Bie, Hendrik; Sommen, Frank Gürlebeck, Klaus; Könke, Carsten VECTOR AND BIVECTOR FOURIER TRANSFORMS IN CLIFFORD ANALYSIS In the past, several types of Fourier transforms in Clifford analysis have been studied. In this paper, first an overview of these different transforms is given. Next, a new equation in a Clifford algebra is proposed, the solutions of which will act as kernels of a new class of generalized Fourier transforms. Two solutions of this equation are studied in more detail, namely a vector-valued solution and a bivector-valued solution, as well as the associated integral transforms. 11 urn:nbn:de:gbv:wim2-20170314-28371 10.25643/bauhaus-universitaet.2837 In Zusammenarbeit mit der Bauhaus-Universität Weimar