Mathematical Research Letters
Volume 7 (2000)
The shape of the error in wavelet approximation and piecewise linear interpolation
Pages: 317 – 327
The graph of the error in wavelet approximation, when properly rescaled, is shown to converge in the Hausdorff metric to a limit set $\Gamma$. The limit set $\Gamma$ is not a graph of a function, but rather a region bounded by the graphs of multiples of a derivative of the function, depending on the first nonvanishing moment of the wavelet. A similar result is shown for piecewise linear interpolation. Higher dimensional analogs are discussed.