Journal of Fourier Analysis and Applications

, Volume 17, Issue 2, pp 240–264 | Cite as

Sampling Theorem and Discrete Fourier Transform on the Hyperboloid



Using Coherent-State (CS) techniques, we prove a sampling theorem for holomorphic functions on the hyperboloid (or its stereographic projection onto the open unit disk \(\mathbb{D}_{1}\)), seen as a homogeneous space of the pseudo-unitary group SU(1,1). We provide a reconstruction formula for bandlimited functions, through a sinc-type kernel, and a discrete Fourier transform from N samples properly chosen. We also study the case of undersampling of band-unlimited functions and the conditions under which a partial reconstruction from N samples is still possible and the accuracy of the approximation, which tends to be exact in the limit N→∞.


Holomorphic functions Coherent states Discrete Fourier transform Sampling Discrete frames 

Mathematics Subject Classification (2000)

32A10 42B05 94A12 94A20 81R30 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • M. Calixto
    • 1
  • J. Guerrero
    • 2
  • J. C. Sánchez-Monreal
    • 1
  1. 1.Departamento de Matemática Aplicada y EstadísticaUniversidad Politécnica de CartagenaCartagenaSpain
  2. 2.Departamento de Matemática Aplicada, Facultad de InformáticaUniversidad de MurciaMurciaSpain

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