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PERTURBATION OF NONHARMONIC FOURIER SERIES AND NONUNIFORM SAMPLING THEOREM

  • Published : 2007.05.31

Abstract

For an entire function f whose Fourier transform has a compact support confined to $[-{\pi},\;{\pi}]$ and restriction to ${\mathbb{R}}$ belongs to $L^2{\mathbb{R}}$, we derive a nonuniform sampling theorem of Lagrange interpolation type with sampling points ${\lambda}_n{\in}{\mathbb{R}},\;n{\in}{\mathbb{Z}}$, under the condition that $$\frac{lim\;sup}{n{\rightarrow}{\infty}}|{\lambda}_n-n|<\frac {1}{4}$.

Keywords

Riesz basis;frame;nonuniform sampling;nonharmonic Fourier series

References

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  2. Multivariate polynomial interpolation and sampling in Paley–Wiener spaces vol.164, pp.4, 2012, https://doi.org/10.1016/j.jat.2011.12.004
  3. Perturbed sampling formulas and local reconstruction in shift invariant spaces vol.377, pp.2, 2011, https://doi.org/10.1016/j.jmaa.2010.12.011