Spectral deviation of concentration operators for the short-time Fourier transform

Abstract. Time-frequency concentration operators restrict the integral analysis-synthesis formula for the short-time Fourier transform to a given compact domain. 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 approximately match known asymptotics. We also consider window functions that decay only polynomially in time and frequency.

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