Classes of uniform convergence of spectral expansions for the one-dimensional Schrödinger operator with a distribution potential

For the self-adjoint Schrödinger 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.