  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.
