Nonuniform Sampling and Multiscale Computation

@article{Engquist2013NonuniformSA,
  title={Nonuniform Sampling and Multiscale Computation},
  author={Bj{\"o}rn Engquist and Christina Frederick},
  journal={Multiscale Model. Simul.},
  year={2013},
  volume={12},
  pages={1890-1901}
}
In homogenization theory and multiscale modeling, typical functions satisfy the scaling law $f^{\epsilon}(x) = f(x,x/\epsilon)$, where $f$ is periodic in the second variable and $\epsilon$ is the smallest relevant wavelength, $0<\epsilon\ll1$. Our main result is a new $L^{2}$-stability estimate for the reconstruction of such bandlimited multiscale functions $f^{\epsilon}$ from periodic nonuniform samples. The goal of this paper is to demonstrate the close relation between and sampling… 

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