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The Funk‐Hecke type relations and ray transforms for the vector spherical wave functions
Author(s) -
Balandin A. L.
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7475
Subject(s) - mathematics , mathematical analysis , type (biology) , fourier transform , pure mathematics , vector valued function , spherical mean , ecology , biology
The Funk‐Hecke type integral relations for vector spherical wave functions are derived. Applying the obtained Funk‐Hecke integral identities, 3D Fourier transforms of vector spherical wave functionsM l m τandN l m τandL l m τare obtained. On the basis of the Central Slice Theorem, the ray transforms for these vector functions are evaluated. This was found to be a useful tool in the scattering and the vector tomography problems.