Abstract:
In the article, we introduce generalizations of
the curl operator acting on three-dimensional symmetric $m$-tensor
fields and establish properties of them. For the spaces of
three-dimensional tensor fields, new detailed decompositions are
obtained. Each term in the decompositions is constructed using of
one function. Decompositions of this kind play a special role, in
particular, in the study of tomographic integral operators acting
on symmetric $m$-tensor fields, $m\geqslant1$, and in the
construction of algorithms for solving the emerging inverse
problems.
Keywords:decomposition of symmetric tensor field,
solenoidal field, potential field, potential, curl operator,
computerized tomography, ray transform, Radon transform.
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