Physics – Mathematical Physics
Scientific paper
2006-12-15
J. Fourier. Anal. Appl. 14, 538-567 (2008)
Physics
Mathematical Physics
26 latex pages. Final version published in J. Fourier Anal. Appl
Scientific paper
10.1007/s00041-008-9027-z
Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) 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 fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann sphere, with spins up to $J$, is also considered. The connection with the standard Euler angle picture, in terms of spherical harmonics, is established through a discrete Bargmann transform.
Calixto Manuel
Guerrero Julio
Sánchez-Monreal Juan Carlos
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