LAUSR

We define the accumulated spectrogram associated to a locally trace–class orthogonal projection operator and a bounded set using the polar decomposition of its restriction on that set. We prove a convergence theorem for accumulated spectrograms along an exhaustion. We show that a radial determinantal point process on Rd is always hyperuniform along the exhaustion formed by the dilations of a bounded open set, and as a consequence, we obtain that dilations of the corresponding accumulated spectrogram converge to the indicator function of the considered set, establishing a universal phenomenon. Our result is a generalization of a theorem in Abreu, Gröchenig, and Romero, [Trans. Am. Math. Soc. 368, 3629–3649 (2016)] concerning time-frequency localization operators.