"Eigenvalue estimates for Fourier concentration operators on two domains"Speckbacher, MichaelIn this presentation, we consider concentration operators associated with either the discrete or the continuous multidimensional Fourier transform, that is, operators that incorporate a spatial cut-off and a subsequent frequency cut-off to the Fourier inversion formula. We derive eigenvalue estimates that quantify the extent to which Fourier concentration operators deviate from orthogonal projectors by bounding the number of eigenvalues away from 0 and 1 in terms of the geometry of the spatial and frequency domains, and a factor that grows at most poly-logarithmically on the inverse of the spectral margin. The estimates are non-asymptotic and almost match asymptotic benchmarks. Our work covers for the first time non-convex and nonsymmetric spatial and frequency concentration domains, as demanded by numerous applications. |
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