A robust method for accurately representing nonperiodic functions given Fourier coefficient information
Many attempts were made to recover accurate and fast converging Fourier series representations for functions exhibiting a Gibbs phenomenon and many methods were derived in the past. Here this problem is treated from the point of view of bounds of the operators corresponding to the methods of suppressing the Gibbs oscillations. Explicit bounds are proven for the operator that corresponds to a least squares fitting of the Fourier coefficients with splines allowing for certain discontinuities.
scientific article; zbMATH DE number 1758462