Del Prete, Vincenza The Slepian property for a class of time-frequency localization operators on the hyperbolic space. (English) Zbl 0888.43003 Boll. Unione Mat. Ital., VII. Ser., B 11, No. 1, 119-139 (1997). Let \(E\) denote the filtered Fourier transform. The problem of signal analysis of constructing the spectral resolution of the compact time-frequency localization operators \(E^*E\) and \(EE^*\) has been solved for the one-dimensional Fourier transform and a sharp edged filter by finding a second order linear differential operator that commutes with the integral operator \(E^*E\) and therefore admits the same eigenfunctions [D. Slepian, H. O. Pollak, Bell System Tech. J. 40, 43-63 (1961; Zbl 0184.08601); H. J. Landau, H. O. Pollak, Bell System Tech. J. 40, 65-84 (1961; Zbl 0184.08602); H. J. Landau, H. O. Pollak, Bell System Tech. J. 41, 1295-1336 (1962; Zbl 0184.08603)]. The purpose of the paper under review is an extension to more general classes of filters and radial functions on the three-dimensional hyperbolic space. The proof depends upon an isometric isomorphism transforming the space of radial square integrable functions on the unit ball \(\mathbb{B}_3\) under its Riemannian structure onto the analog space of functions on the three-dimensional Euclidean vector space. Reviewer: W.Schempp (Siegen) MSC: 43A32 Other transforms and operators of Fourier type 94A12 Signal theory (characterization, reconstruction, filtering, etc.) 43A85 Harmonic analysis on homogeneous spaces Keywords:filtered Fourier transform; signal analysis; spectral resolution; time-frequency localization operators; hyperbolic space Citations:Zbl 0184.08601; Zbl 0184.08602; Zbl 0184.08603 PDFBibTeX XMLCite \textit{V. Del Prete}, Boll. Unione Mat. Ital., VII. Ser., B 11, No. 1, 119--139 (1997; Zbl 0888.43003)