Nonlinear inversion of a band-limited Fourier transform
For a compactly supported function with singularities, this current paper defines two rational approximations based on values of its Fourier transform in a bounded interval, and several Fourier coefficients respectively (the function is extended to periodic one in the second case). It turns out that both approximations avoid Gibbs phenomenon, the poles of rational representations indicate singularity locations of the function, and the approximation errors away from singularities behave as that of uniform approximations. The same method can be used to discuss the impact of adding white noise to the Fourier data, and to estimate density of eigenvalues of Hermitian operators.
scientific article; zbMATH DE number 5618751
scientific article