Spectral deviation of concentration operators for the short-time Fourier transform
Volume 270 / 2023
Studia Mathematica 270 (2023), 145-173
MSC: Primary 47B35; Secondary 47G30, 42B35, 47A75, 42C40.
DOI: 10.4064/sm220214-17-10
Published online: 12 December 2022
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 almost match known asymptotics, with the advantage of being effective for concrete domains and spectral thresholds. As such our estimates allow for applications where the spectral threshold depends on the geometry of the time-frequency concentration domain. We also consider window functions that decay only polynomially in time and frequency.
