Fridman, Buma; Kuchment, Peter; Lancaster, Kirk; Lissianoi, Serguei; Mogilevsky, Mila Numerical harmonic analysis on the hyperbolic plane. (English) Zbl 1022.65145 Appl. Anal. 76, No. 3-4, 351-362 (2000). Summary: Results are reported of a numerical implementation of the hyperbolic Fourier transform and the geodesic and horocyclic Radon transforms on the hyperbolic plane, and of their inverses. The study is motivated by the hyperbolic geometry approach to the linearized inverse conductivity problem, suggested by C. A. Berenstein and E. Casadio Tarabusi [Lect. Notes Math. Phys. 4, 39-44 (1994; Zbl 0826.35132); SIAM J. Appl. Math. 56, No. 3, 755-764 (1996; Zbl 0854.35124)]. Cited in 5 Documents MSC: 65T40 Numerical methods for trigonometric approximation and interpolation 43A85 Harmonic analysis on homogeneous spaces 32A38 Algebras of holomorphic functions of several complex variables 65R32 Numerical methods for inverse problems for integral equations 65R10 Numerical methods for integral transforms 44A12 Radon transform 92C55 Biomedical imaging and signal processing Keywords:inverse transform; impedance imaging; tomography; hyperbolic Fourier transform; geodesic and horocyclic Radon transforms; hyperbolic plane Citations:Zbl 0826.35132; Zbl 0854.35124 PDFBibTeX XMLCite \textit{B. Fridman} et al., Appl. Anal. 76, No. 3--4, 351--362 (2000; Zbl 1022.65145) Full Text: DOI References: [1] Panasenko G.P., C.R.Acad.Sci.Paris, t 326 pp 867– (1998) [2] Panasenko G.P., C.R.Acad.Sci.Paris, t 326 pp 893– (1998) [3] Panasenko G.P., Porous Media: Physics, Models, Simulation pp 217– (1999) [4] Panasenko G.P., C.R.Acad.Sci.Paris, t 327 pp 1185– (1999) [5] Blanc F F., Mathematical Models and Methods in Applied Sciences 9 (1999) [6] Nazarov S.A., Boundary value problems for Lamé operator, St. Petersburg Math. Journal 8 pp 879– (1997) [7] Specovius Neugebauer M., University of Paderborn (1997) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.