@inproceedings{DeBieSommen, author = {De Bie, Hendrik and Sommen, Frank}, title = {VECTOR AND BIVECTOR FOURIER TRANSFORMS IN CLIFFORD ANALYSIS}, editor = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten}, organization = {Bauhaus-Universit{\"a}t Weimar}, issn = {1611-4086}, doi = {10.25643/bauhaus-universitaet.2837}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28371}, pages = {11}, abstract = {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.}, subject = {Angewandte Informatik}, language = {en} }