Classes of Uniform Convergence of Spectral Expansions for the One-Dimensional Schrodinger Operator with a Distribution Potential

For the self-adjoint Schrodinger operator L defined on R by the differential operation -(d/dx)(2) + q(x) with a distribution potential q(x) uniformly locally belonging to the space W-2(-1), we describe classes of functions whose spectral expansions corresponding to the operator L absolutely and uniformly converge on the entire line R. We characterize the sharp convergence rate of the spectral expansion of a function using a two-sided estimate obtained in the paper for its generalized Fourier transforms.