Nonharmonic nonlinear Fourier frames and convergence of corresponding frame series

Abstract

Having redundancy, frames, compared with basis, can provide more robust representation of a vector in application. By introducing nonharmonic nonlinear Fourier frames, a method is established to construct such frames by perturbation. Based on a special class of nonharmonic nonlinear Fourier frames, the convergence of its corresponding frame operator is investigated, and the convergence rate, associated with the coefficient sequence of the frame operator, is estimated. Finally, we also discuss the equiconvergence of two different (nonlinear or linear) Fourier (basis or frame) series of f ∈ L² (−π,π).