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# Mathematical Research Letters

## Volume 7 (2000)

### Number 3

### The shape of the error in wavelet approximation and piecewise linear interpolation

Pages: 317 – 327

DOI: http://dx.doi.org/10.4310/MRL.2000.v7.n3.a6

#### Author

#### Abstract

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.