Normal operators for momentum ray transforms, I: The inversion formula

The momentum ray transform \(I_m^k\) integrates a rank \(m\) symmetric tensor field \(f\) on \(\mathbb R^n\) over lines with the weight \(t^k\), \(I_m^kf(x,\xi)=\int_{-\infty}^\infty t^k\langle f(x+t\xi),\xi^m\rangle\,\mathrm{d}t\). We compute the normal operator \(N_m^k=(I_m^k){}^*I_m^k\) and present an inversion formula recovering a rank \(m\) tensor field \(f\) from the data \((N_m^0f,\dots,N_m^mf)\).