Some properties of spectral expansions related to the one-dimensional Stark effect Hamiltonian

We consider the one-dimensional Stark effect Hamiltonian defined over the whole line R by the differential expression Hu = −u″ + Exu + q(x)u, E ≠ 0. This paper analyses the equiconvergence property of the related spectral expansion with the Fourier integral expansion in the uniform over any compact set or over the whole line R metric.