2025/02/17 by Halvdansson, Simon
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2502.11805
For time-frequency localization operators, related to the short-time Fourier transform, with symbol RΩ, we work out the exact large R eigenvalue behavior for rotationally invariant Ω and conjecture that the same relation holds for all scaled symbols R Ω as long as the window is the standard Gaussian. Specifically, we conjecture that the k-th eigenvalue of the localization operator with symbol RΩ converges to (1)/(2)erfc( √(2π)(k-R2|Ω|)/(R|∂ Ω|) ) as R → ∞. To support the conjecture, we compute the eigenvalues of discrete frame multipliers with various symbols using LTFAT and find that they agree with the behavior of the conjecture to a large degree.