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Multiresolution on the Sphere

  • Matthias Conrad
  • Jürgen Prestin
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

In this paper we study some basic tools for the construction of multi-scale systems on the unit sphere. Particularly, we emphasize properties of spherical harmonics and Legendre functions. Based on these orthogonal systems we discuss in some detail the decomposition of the classical Hilbert space on the sphere into subspaces of different level. To this end we explain different bases and frames. In our examples the building blocks consist of polynomials and spherical radial basis functions.

Keywords

Spherical Harmonic Tight Frame Refinement Grid Positive Definiteness Addition Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Matthias Conrad
    • 1
  • Jürgen Prestin
    • 2
  1. 1.FB InformatikUniversity of HamburgGermany
  2. 2.Institute of MathematicsMedical University of LübeckGermany

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