Ag. Ramm, INVERSION-FORMULA AND SINGULARITIES OF THE SOLUTION FOR THE BACKPROJECTION OPERATOR IN TOMOGRAPHY, Proceedings of the American Mathematical Society, 124(2), 1996, pp. 567-577
Let R mu := integral(S2) mu(alpha, alpha . x)d alpha, x is an element
of R(n), be the backprojection operator. The range of this operator a
s an operator on non-smooth functions R : X := L(0)(infinity) (S-n-1
X R) --> L(loc)(2) (R(n)) is described and formulas for (R)(-1) are d
erived. It is proved that the operator R is not injective on X but is
injective on the subspace X(e) of X which consists of even functions
mu(alpha, p) = mu(-alpha, -p). Singularities of the function (R)(-1)
h are studied. Here h is a piecewise-smooth compactly supported functi
on. Conditions for mu to have compact support are given. Some applicat
ions are considered.