caa a22 4500 477094589 CHVBK 20180405111524.0 cr unu---uuuuu 170330e19960501xx s 000 0 eng 10.1007/BF03322229 doi (NATIONALLICENCE)springer-10.1007/BF03322229 Rosier Michael Tannenbergstr. 2, 58706, Menden aut Biorthogonal decompositions of the Radon transform by multivariate interpolation [Elektronische Daten] [Michael Rosier] The concept of biorthogonal and singular value decompositions is a valuable tool in the examination of ill-posed inverse problems such as the inversion of the Radon transform. By application of the theory of multivariate interpolation, e. g. the set of Lagrange polynomials with respect to the space of homogeneous spherical polynomials, we determine new biorthogonal decompositions of the Radon transform. We consider the case of functions with support in the unit ball and the case of functions with support ℝr. In both cases we assume that the functions are square integrable with respect to some weight functions. In the important special case of square integrable functions with respect to the unit ball the structure of the biorthogonal decompositions is easier in comparison with the known singular and biorthogonal decompositions. Especially the calculation of the unknown expansion coefficients can be done by using arbitrary fundamental systems (μ-resolving data set in terms of tomography with a minimum number of nodes) and simplifies essentially. The decompositions are based on a system of zonal (ridge) Gegenbauer (ultraspherical) polynomials which are used in the theory of the Radon transform and in the field of numerical algorithms for the inversion of the transform. Birkhäuser Verlag, Basel, 1996 Radon transform nationallicence singular value decomposition nationallicence biorthogonal decomposition nationallicence biorthogonal polynomial nationallicence multivariate interpolation nationallicence Results in Mathematics Birkhäuser-Verlag 29/3-4(1996-05-01), 335-354 0378-6218 29:3-4<335 1996 29 25 https://doi.org/10.1007/BF03322229 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF03322229 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rosier Michael Tannenbergstr. 2, 58706, Menden aut NATIONALLICENCE 773 0- Results in Mathematics Birkhäuser-Verlag 29/3-4(1996-05-01), 335-354 0378-6218 29:3-4<335 1996 29 25 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer