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Numerical harmonic analysis on the hyperbolic plane. (English) Zbl 1022.65145

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)].

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
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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)
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[7] Specovius Neugebauer M., University of Paderborn (1997)
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