TY - JOUR 
A1 - Guerrero García, Julio
AU - Sánchez Monreal, Juan Carlos
AU - Calixto Molina, Manuel
T1 - Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere
Y1 - 2008
SN - 1069-5869
UR - http://hdl.handle.net/10317/525
UR - arXiv:math-ph/0612046v1
AB - 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.
KW - Matemática Aplicada
KW - Transformacion rápida de Fourier
KW - Esferas Riemann
KW - Armónicos esféricos
KW - Funciones Majorana
KW - Matrices circulantes
KW - Matrices rectangulares de Fourier
LA - eng
PB - Springer
ER -