Semi-continuous and discrete wavelet frames on $n$-dimensional spheres

Abstract

The paper shows that under some mild conditions $n$-dimensional spherical wavelets derived from approximate identities build semi-continuous frames. Moreover, for sufficiently dense grids Poisson wavelets on $n$-dimensional spheres constitute a discrete frame. In the proof we only use the localization properties of the reproducing kernel and its gradient.

28 pages

References in corpus (3)

• Continuous Wavelets on Compact Manifolds
• Continuous wavelet transforms on $n$-dimensional spheres
• Poisson wavelets on $n$-dimensional spheres

Cited by in corpus (5)

• Frames of directional wavelets on $n$-dimensional spheres
• Directional wavelets on $n$-dimensional spheres
• Uncertainty of Poisson wavelets
• Uncertainty product of spherical wavelets
• Angular multiselectivity with spherical wavelets