In this paper, an inversion problem for the weighted Radon transform along family of cones in threedimensional space is considered. An inversion formula for the weighted Radon transform is obtained for the case when the range is a space of infinitely smooth functions. KEYWORDS integral geometry problem, weighted Radon transform, inversion formula ACKNOWLEDGEMENTS Authors partially supported by the grant FZ-20200929224 of Fundamental Science Foundation of Uzbekistan. Authors thank the referee for valuable comments and gratefully acknowledge. FOR CITATION Muminov M.I., Ochilov Z.Kh. An inversion formula for the weighted Radon transform along family of cones.

The two-particle Schr ödinger operator h µ (k), k ∈ T d (where µ > 0, T d is a d-dimensional torus), associated to the Hamiltonian h of the system of two quantum particles moving on a d-dimensional lattice, is considered as a perturbation of free Hamiltonian h 0 (k) by the certain 3 d rank potential operator µv. The existence conditions of eigenvalues and virtual levels of h µ (k), are investigated in detail with respect to the particle interaction µ and total quasi-momentum k ∈ T d . KEYWORDS two-particle Hamiltonian, invariant subspace, orthogonal projector, eigenvalue, virtual level, multiplicity of virtual level. d α=1 µ α cos(p α − q α ) was investigated in [17]. Detailed spectral properties of the