Abstract
The uncertainty principle in Fourier analysis sets a limit to the possible simultaneous concentration of a function and its Hankel transform. Nevertheless, signals that have highly concentrated time-frequency content have many applications in quantum mechanics, PDE, engineering and in signal analysis. We use here time-frequency localization operators in the Hankel setting to measure the time-frequency content of functions on a subset of finite measure Sigma within the time-frequency plane. Then, using eigenfunctions and eigenvalues of these operators, we prove a characterization of functions that are time-frequency concentrated in Sigma, and we obtain approximation inequalities for such functions using a finite linear combination of eigenfunctions, since they are maximally time-frequency-concentrated in the region of interest.