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Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomor-phic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of N samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over-and under-sampling. Sample points are roots of unity, a(More)
In this paper we are mainly concerned with the study of polarizations (in general of higher-order type) on a connected Lie group with a U(1)-principal bundle structure. The representation technique used here is formulated on the basis of a group quantization formalism previously introduced which generalizes the Kostant-Kirillov co-adjoint orbits method for(More)
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical values of the anomaly leads to a new degree of freedom which shares its internal character with spin, but nevertheless(More)
We present a unified group-theoretical derivation of the Continuous Wavelet Transform (CWT) on the circle S 1 and the real line R, following the general formalism of Coherent States (CS) associated to unitary square integrable (modulo a subgroup, possibly) representations of the group SL(2, R). A general procedure for obtaining unitary representations of a(More)
We implement a finite-dimensional representation of the 2+1D Lorentz group with a PT-symmetric waveguide array. Our device can be engineered to behave like a multi-port oscillator or directional coupler with amplification. We show that the two-waveguide coupler with linear losses, the Vernier effect in coupled asymmetric micro-cavity lasers, and the(More)