Preprint Number 10–21 LANDAU’S NECESSARY DENSITY CONDITIONS FOR THE HANKEL TRANSFORM

Abstract: We will prove an analogue of Landau’s necessary conditions [Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967).] for spaces of functions whose Hankel transform is supported in a measurable subset S of the positive semi-axis. As a special case, necessary density conditions for the existence of Fourier-Bessel frames are obtained. In the course of our proof we obtain estimates for some eigenvalues which arise in Tracy and Widom work [Level spacing distributions and the Bessel kernel. Comm. Math. Phys. 161 (1994), no. 2, 289–309.]