Density Theorems for Nonuniform Sampling of Bandlimited Functions Using Derivatives or Bunched Measurements

@article{Adcock2014DensityTF,
  title={Density Theorems for Nonuniform Sampling of Bandlimited Functions Using Derivatives or Bunched Measurements},
  author={B. Adcock and M. Gataric and A. Hansen},
  journal={Journal of Fourier Analysis and Applications},
  year={2014},
  volume={23},
  pages={1311-1347}
}
  • B. Adcock, M. Gataric, A. Hansen
  • Published 2014
  • Mathematics
  • Journal of Fourier Analysis and Applications
  • We provide sufficient density condition for a set of nonuniform samples to give rise to a set of sampling for multivariate bandlimited functions when the measurements consist of pointwise evaluations of a function and its first k derivatives. Along with explicit estimates of corresponding frame bounds, we derive the explicit density bound and show that, as k increases, it grows linearly in $$k+1$$k+1 with the constant of proportionality $$1/\mathrm {e}$$1/e. Seeking larger gap conditions, we… CONTINUE READING
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