Weighted Eigenfunction Estimates with Applications to Compressed Sensing

@article{Burq2012WeightedEE,
  title={Weighted Eigenfunction Estimates with Applications to Compressed Sensing},
  author={Nicolas Burq and Semyon Dyatlov and Rachel A. Ward and Maciej Zworski},
  journal={SIAM J. Math. Anal.},
  year={2012},
  volume={44},
  pages={3481-3501}
}
Using tools from semiclassical analysis, we give weighted L^\infty estimates for eigenfunctions of strictly convex surfaces of revolution. These estimates give rise to new sampling techniques and provide improved bounds on the number of samples necessary for recovering sparse eigenfunction expansions on surfaces of revolution. On the sphere, our estimates imply that any function having an s-sparse expansion in the first N spherical harmonics can be efficiently recovered from its values at m > s… 

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