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A Reconstruction Method for Band-limited Signals on the Hyperbolic Plane

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Abstract

A notion of band limited functions is considered in the case of the hyperbolic plane in its Poincare upper half-plane ℍ realization. The concept of band-limitedness is based on the existence of the Helgason-Fourier transform on ℍ. An iterative algorithm is presented, which allows to reconstruct band-limited functions from some countable sets of their values. It is shown that for sufficiently dense metric lattices a geometric rate of convergence can be guaranteed as long as the sampling density is high enough compared to the band-width of the sampled function.

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Authors and Affiliations

  1. Department of Mathematics, Vienna University, Austria

    Hans Feichtinger

  2. Department of Mathematics, Temple University, Philadelphia, PA, 19122, USA

    Isaac Pesenson

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  1. Hans Feichtinger
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  2. Isaac Pesenson
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Correspondence to Hans Feichtinger.

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Feichtinger, H., Pesenson, I. A Reconstruction Method for Band-limited Signals on the Hyperbolic Plane. STSIP 4, 107–119 (2005). https://doi.org/10.1007/BF03549428

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