Inversion of the ray transform of scalar and vector fields.
Main publications:
E. V. Arbuzov and A. L. Bukhgeim and S. G. Kazantsev, “Two-dimensional tomography problems and the theory of A-analytic functions”, Siberian Adv. Math., 8:4 (1998), 1–20
S. G. Kazantsev and A. A. Bukhgeim, “Singular value decomposition of the 2D fan-beam Radon transform of tensor fields”, J. Inv. Ill-Posed Problems, 12:3 (2004), 245–278
E. Yu. Derevtsov, S. G. Kazantsev, Th. Schuster, “Polynomial bases for subspaces of vector fields in the unit ball. Method of ridge functions”, J. Inv. Ill-Posed Problems, 15:1 (2007), 19–55
S. G. Kazantsev and A. A. Bukhgeim, “Inversion of the Scalar and Vector Attenuated X-Ray Transforms in a Unit Disc”, J. Inv. Ill-Posed Problems, 15:7 (2007), 735–765
S. G. Kazantsev, “Factorization of the Green's operator in the Dirichlet problem for $(-1)^m(d/d t)^{2m}$”, Sib. Èlektron. Mat. Izv., 16 (2019), 1662–1688
2.
S. G. Kazantsev, V. B. Kardakov, “Poloidal-toroidal decomposition of solenoidal vector fields in the ball”, Sib. Zh. Ind. Mat., 22:3 (2019), 74–95; J. Appl. Industr. Math., 13:3 (2019), 480–499
S. G. Kazantsev, “Funk–Minkowski transform and spherical convolution of Hilbert type in reconstructing functions on the sphere”, Sib. Èlektron. Mat. Izv., 15 (2018), 1630–1650
S. G. Kazantsev, “Tensor fields on the plane and Riesz transforms”, Sib. Èlektron. Mat. Izv., 11 (2014), 709–724
2013
5.
D. S. Anikonov, S. G. Kazantsev, D. S. Konovalova, “An inverse problem of location type for a hyperbolic system”, Sib. Zh. Ind. Mat., 16:4 (2013), 3–20
D. S. Anikonov, S. G. Kazantsev, D. S. Konovalova, “Differential properties of a generalized solution to a hyperbolic system of first-order differential equations”, Sib. Zh. Ind. Mat., 16:2 (2013), 26–39; J. Appl. Industr. Math., 7:3 (2013), 313–325
A. L. Bukhgeim, S. G. Kazantsev, “Elliptic systems of Beltrami type and tomography problems”, Dokl. Akad. Nauk SSSR, 315:1 (1990), 15–19; Dokl. Math., 42:3 (1991), 704–707
Contact us: