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Using coherent-state techniques, we prove a sampling theorem for Majorana's(holomorphic) functions on the Riemann sphere and we provide an exactreconstruction formula as a convolution product of $N$ samples and a givenreconstruction kernel (a sinc-type function). We also discuss the effect ofover- and under-sampling. Sample points are roots of unity, a fact which allowsexplicit inversion formulas for resolution and overlapping kernel operatorsthrough the theory of Circulant Matrices and Rectangular Fourier Matrices. Thecase of band-limited functions on the Riemann sphere, with spins up to $J$, isalso considered. The connection with the standard Euler angle picture, in termsof spherical harmonics, is established through a discrete Bargmann transform.Comment: 26 latex pages. Final version published in J. Fourier Anal. App

Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere