Weighted eigenfunction estimates with applications to compressed sensing

Abstract

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 N^(1/6) log^4(N) sampling points.

25 pages, 5 figures

References in corpus (3)

• Sparse recovery for spherical harmonic expansions
• Quasi-normal modes and exponential energy decay for the Kerr-de Sitter black hole
• CMB data analysis and sparsity

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• Uniform pointwise estimates for ultraspherical polynomials
• Tight bounds on the mutual coherence of sensing matrices for Wigner D-functions on regular grids