Voir la notice de l'article provenant de la source Math-Net.Ru
@article{SJVM_2009_12_2_a1, author = {A. L. Balandin}, title = {Vector spherical harmonics {in~3-D} vector tomography}, journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki}, pages = {131--143}, publisher = {mathdoc}, volume = {12}, number = {2}, year = {2009}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/SJVM_2009_12_2_a1/} }
A. L. Balandin. Vector spherical harmonics in~3-D vector tomography. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 2, pp. 131-143. http://geodesic.mathdoc.fr/item/SJVM_2009_12_2_a1/
[1] Blatt D. Zh., Vaiskopf V., “Prilozhenie II”, Teoreticheskaya yadernaya fizika, IL, Moskva, 1954
[2] Gel'fand I. M., Shapiro Z. Y., “Representation of the group of rotation in three-dimensional space and their applications”, Am. Math. Soc. Transl., 2, 1956, 207–316 | MR
[3] Edmonds A. R., Angular Momentum in Quantum Mechanics, University Press, Prinston, 1957 | MR | Zbl
[4] Freeden W., Gervens T., Schreiner M., Constructive Approximation on the Sphere (With Applications to Geomathematics), Oxford Science Publication, Clarendon Press, 1998 | MR | Zbl
[5] Godunov S. K., Mikhailova T. Yu., Predstavleniya gruppy vrascheniya i sfericheskie funktsii, Nauchnaya kniga, Novosibirsk, 1998 | MR | Zbl
[6] Moses H. E., “The use of vector spherical harmonics in global meteorology and aeronomy”, J. Atmospheric Sci., 31 (1974), 1490–1500 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR
[7] Hill E. H., “The theory of vector spherical harmonics”, Amer. J. Phys., 22 (1953), 211–214 | DOI | MR
[8] Mors F. M., Feshbakh G., Metody teoreticheskoi fiziki, T. 1, IL, M., 1958
[9] Varshalovich D. A., Moskalev A. N., Khersonskii V. K., Kvantovaya teoriya uglovogo momenta, Nauka, L., 1975
[10] Balandin A. L., Ono Y., “The method of series expansion for 3-D vector tomography reconstruction”, J. Computational Physics, 202 (2005), 52–64 | DOI | MR | Zbl
[11] Natterer F., Wübbeling F., Mathematical Methods in Image Reconstruction, SIAM, Philadelphia, 2001 | MR
[12] Bidenkharn L., Lauk Dzh., Uglovoi moment v kvantovoi fizike. Teoriya i prilozheniya, T. 1, Mir, M., 1984
[13] Temam P., Navier–Stoks Equations, Theory and Numerical Analysis, Noth-Holland Publ., Amsterdam, 1979 | MR | Zbl
[14] Derevtsov E. Yu., Kazantsev S. G., Schuster Th., “Polynomial bases for subspaces of vector fields in the unit ball. Method of ridge functions”, J. Ill-Posed Problems, 15:1 (2007), 19–55 | DOI | MR | Zbl
[15] Kazantsev S. G., Bukhgeim A. A., “The chebyshev ridge polynomials in 2D tensor tomography”, J. Ill-Posed Problems, 14:2 (2006), 157–188 | DOI | MR | Zbl
[16] Cantarella J., DeTurck D., Gluck H., “Vector calculus and the topology of domains in 3-space”, Amer. Math. Month., 109:5 (2002), 409–442 | DOI | MR | Zbl
[17] Sharafutdinov V. A., Integralnaya geometriya tenzornykh polei, VO “Nauka”, Novosibirsk, 1993 | MR | Zbl
[18] Björck, Åke, Numerical Methods for Least Squares Problems, SIAM, Philadelphia, 1996 | MR | Zbl
[19] Wang Ling, “The X-ray transform and its inversion for the series expansion basis functions in three-dimensional tomography”, SIAM J. Appl. Math., 52:5 (1992), 1490–1499 | DOI | MR | Zbl
[20] Bellan Paul M., Fundamentals of Plasma Physics, Cambridge Univ. Press, Cambridge, 2006