Limit theorems for Fourier transforms of functionals of Gaussian sequences

Summary Limit theorems with a non-Gaussian (in fact nonstable) limiting distribution have been obtained under suitable conditions for partial sums of instantaneous nonlinear functions of stationary Gaussian sequences with long range dependence. Analogous limit theorems are here obtained for finite Fourier transforms of instantaneous nonlinear functions of stationary Gaussian sequences with long range dependence.Research supported in part by the Office of Naval Research Contract N00014-75C-0428.