"Spectral deviation of concentration operators for the short-time Fourier transform"Marceca, FelipeTime-frequency concentration operators restrict the integral analysis-synthesis formula for the short-time Fourier transform to a given compact domain. In this talk we estimate how much the corresponding eigenvalue counting function deviates from the Lebesgue measure of the time-frequency domain. For window functions in the Gelfand-Shilov class, the bounds almost match known asymptotics, with the advantage of being effective for concrete domains and values of the eigenvalue counting function. We also consider window functions that decay only polynomially in time and frequency. |
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